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9 December 2025

The Effect of Foreign Influence on Conflict and Social Identity in Ethnically Diverse Societies †

Institute of Economic Analysis Spanish Research Council and Barcelona School of Economics, Campus UAB, 08193 Bellaterra, Barcelona, Spain
A former version of the paper was circulated under the title “Foreign Influence and Identity Equilibria: A Model of External Intervention and Social Alignement”.

Abstract

This paper develops a formal model to analyze how foreign interventions—via resource transfers towards mobilization, technological upgrades of the mobilization technology, and various forms of conditional aid—reshape identity choices and conflict dynamics in divided societies. After a foreign intervention occurred, individuals simultaneously decided how many resources to allocate to conflict and whether to identify as ethnic or national. The utility derived from identity decreases with the perceived social distance from the chosen group and increases with the group’s status. Foreign interventions can modify identity choices by affecting perceived social distance or group status. Our results reveal that inclusive aid and material support for mobilization are likely to induce national identification. Conversely, exclusive or ethnically targeted aid and technological upgrades of mobilization technology are likely to result in ethnic identification. We show that for all types of interventions analyzed, conflict mobilization is lower and the intervened nation’s material payoff is higher when individuals identify nationally than ethnically.

1. Introduction

While foreign interventions are frequent (see Aidt et al. (2021) for an overview), external actors—states, parties, firms, diasporas, and transnational movements—rarely intervene in other polities as neutral bystanders. They provide money, organizational capacity, technologies, media narratives, and conditional assistance that reshape not only material payoffs but also who people think they are and with whom they align. Because identity choices co-determine conflict, it is important to analyze how foreign influence affects social identification to fully understand the impact of a foreign intervention.
To study this question, we use a utility function introduced by Shayo (2009), which accounts for both material payoffs and social identity.1 In this framework, individuals derive utility not only from their economic outcomes but also from their identification with a social group. Drawing on robust findings from social psychology, such as the minimal group paradigm and conceptual similarity theories (e.g., Nosofsky, 1986), the utility derived from identity decreases as the perceived social distance between the individual and their chosen group increases, and it rises with the status of that group.2 Based on this utility function, Sambanis and Shayo (2013) develop a model in which individuals of two ethnic groups in the same nation simultaneously choose (i) resources devoted to political contest or fighting, which we label as “mobilization or conflict resources”, and (ii) a social identity—either ethnic (alignment with group A or B) or national (N).3 We extend this social identity framework by embedding foreign influence along three widely observed channels: (1) interventions that modify the contest success function via resource injections (e.g., funds, logistics) or technology upgrades (e.g., training, targeting tools, organizational methods) and (2) conditional aid tied to political control or to identity itself. Our model allows us to analyze in detail how different foreign influence channels affect mobilization efforts and identity choices.
In our model, ethnic groups are internally homogeneous, whereas the nation is heterogeneous, comprising multiple ethnic groups. Thus, under ethnic identification, perceived social distance is zero, while under national identification, it is positive and entails a cost. Furthermore, social distance rises with ethnic salience, which itself intensifies with the degree of interethnic conflict.
Group status is defined relative to a reference group. It increases with the material payoff of the group with which an individual identifies and decreases with the payoff of the reference group. Under ethnic identification, the reference group is the other ethnic group; under national identification, it is another nation. The resources allocated by a group to mobilization have two opposing effects on its material payoff: they directly reduce the payoff through resource expenditure, yet they indirectly increase it by raising the probability of securing the contested resource via the contest success function. Foreign aid can affect both the size of the contested resource and the conditions under which it is granted, thereby influencing the material payoffs of groups A and B. These payoffs interact with identity choices: under ethnic identification, groups compete through direct comparison, whereas under national identification, they benefit from aggregate material payoffs, as all individuals are part of the nation. We analyze social identity equilibria as defined by Shayo (2009). An equilibrium exists if and only if mobilization and identity choices are mutually optimal. In other words, mobilization efforts must be optimal given the identity choice, and identity choices must be optimal given mobilization efforts. To derive these equilibria, we employ a two-step procedure: first, we determine optimal mobilization efforts while holding identity fixed; second, we verify whether, given these mobilization efforts, the assumed identity choice remains optimal.
Across all foreign interventions analyzed, we find that total mobilization resources are greater under an all-ethnic equilibrium, where all individuals identify ethnically, than under an all-national equilibrium, in which all individuals identify with the nation. Consequently, all-national equilibria are associated with lower conflict intensity compared to all-ethnic equilibria. This generally results in a higher aggregate material payoff for the intervened nation under national identification than under ethnic identification. Hence, interventions that make national identification more likely should be preferred if conflict reduction or the overall material payoff of the intervened country is the ultimate aim.
We show that the provision of external mobilization resources reduces domestic mobilization by the beneficiary (unless the beneficiary had fewer resources than desired to dedicate to the contest) and makes an all-national equilibrium outcome more likely. So do inclusive aid and aid conditional on national identification. In contrast, improvements in the contest technology, exclusive aid, and aid conditional on ethnic identification increase the likelihood of an all-ethnic equilibrium.
The remainder of this paper is organized as follows. Section 2 discusses the related literature. In Section 3, we introduce the basic model. Section 4 discusses foreign influence through the provision of mobilization resources or technological improvements in mobilization technologies, while Section 5 concentrates on different forms of conditional aid. In both sections, we provide some empirical examples that are consistent with our results. Section 6 concludes this paper and discusses additional channels of foreign influence on identity. Most propositions are derived in the Appendices.

3. A Model of Foreign Influence

We extend the model of conflict with the identity concerns proposed in Sambanis and Shayo (2013) to incorporate foreign influence. We conduct this in such a way that when foreign influence is absent—which can be modeled by setting the corresponding influence variables to zero—our model reduces to that of Sambanis and Shayo (2013).
The influenced country consists of a set of M individuals divided into two (sub)groups A and B of equal size that aim to capture the value V from controlling the state. As explained in Sambanis and Shayo (2013), V can be interpreted as tangible, “lootable” resources. However, it can also encompass government policies or resources that, within a given institutional framework, can be allocated to benefit a specific group and whose distribution can be influenced through coercion. Specifically, V may represent the share of government resources that those in power can channel toward their own group (Besley & Persson, 2011) or policies and budgets that produce public goods favoring one group over another.
Each individual i is endowed with some exogenous resource endowment (or income) y i and faces two choices: their contest mobilization, which represents the amount of resources invested into conflict f i 0 , y i over V, and their social identity. All individuals make these choices simultaneously. The set of possible social identities is fixed as G = A , B , N : the individual can either identify on the subgroup level, which we refer to as “ethnic identification” A , B , or as belonging to a unified group N made up of both subgroups, which we label “national or civic identification”. In other words, each individual belongs to their fixed ethnic group (A or B ) and the nation N and chooses their social identity by either identifying ethnically (with its fixed ethnic group) or nationally. Hence the social group to which individual i belongs is G i A , N for i A and G i B , N for i B . We assume that all individuals in the same ethnic group have the same income. National income is Y = Y A + Y B , where Y A = i A y i , and Y B = i B y i .
To model individual utility, we use the utility function proposed by Shayo (2009) which was adapted by Sambanis and Shayo (2013) to an ethnically divided society. This utility function combines material payoff with identity concerns. In particular, it draws on robust findings from social psychology, such as the minimal group paradigm and conceptual similarity theories (e.g., Nosofsky, 1986), which show that individuals derive utility from perceived closeness to social groups and their status. When individuals identify with a group, they receive positive utility from the status S G of the group G = A , B , N they identify with while paying a cognitive cost that increases with the distance d i , G 2 between the individual and the group they identify with. The individual utility function is given by
U i ( f i , G ) = π i β d i , G 2 + γ S G
where β and γ are positive constants and represent the weight given to distance and group status, respectively, and π i denotes the material payoff of individual i. The linear structure ensures analytical tractability, allowing for equilibrium analysis and comparative statics. It generalizes existing frameworks of altruism4 and identity5, by incorporating status-seeking behavior in a parsimonious way that captures trade-offs between material self-interest and identity-based preferences. This structure enables the model to explain why individuals may behave against their economic interests due to identity considerations.
Economic interests are captured by the material payoff, which is given by
π i = y i f i + p i J V
where p i J refers to the probability that i’s subgroup J A , B is victorious or the proportion of V that the subgroup J A , B can capture in the contest.6 The probability p i J is determined by a contest success function which depends on the domestic contest mobilization resources provided by subgroups A and B as well as on a potential foreign intervention that might either provide external mobilization resources (monetary outlays, manpower, logistics, organizational effort, media/campaign activity, etc.) or improve the contest technology (technological upgrades, training, targeting, organizational methods) of the aided group. If the foreign interveners provide mobilization resources, the probability p i J depends on domestic contest mobilization and the potential external mobilization resources received by the subgroups and is defined by the resource mobilization in favor of subgroup J divided by the total mobilization both domestic and foreign in society. F J = i J f i denotes the domestic resource mobilization of subgroup J A , B and E J the external mobilization resources received by subgroup J; thus the success probability in the contest of subgroup J is given by
p i J = F J + E J F + E with J A , B
where F = F J + F J refers to total domestic mobilization and E = E J + E J to total foreign mobilization.7
On the other hand, a foreign improvement in mobilization technology is modeled as raising the effectiveness of the aided group’s domestic mobilization through a technology multiplier α J 1 . We abstract from the resources required to induce this technological improvement and assume that the aided group simply receives the improved technology for its use. In this case,
p i J = α J F J α J F J + α J F J with J A , B
and α J = 1 in the absence of a foreign technological improvement, and α J > 1 under a foreign improvement in the conflict technology used by J.
As in Sambanis and Shayo (2013), each individual is characterized by a set of ethnic attributes and a set of national attributes represented as a binary variable:
q i n = 1 if i N 0 otherwise and q i e = 1 if i A 0 if i B
Social distance is given by
d i , G 2 = w n q i n q G n 2 + w e q i e q G e 2 , G A , B , N
where q G n and q G e are the proportions of agents in group G that have attribute n or e, respectively, and w e , w n 0 are attention weights given to the the ethnic-specific or national attributes, respectively, with w n + w e = 1 . The more salient an attribute, the higher its attention weight. We follow Sambanis and Shayo (2013) in assuming that the salience of the ethnic attribute is weakly increasing in the intensity of interethnic conflict I F .
w e = η 0 + η 1 I F
where η 0 0 , 1 is the relative salience of the ethnic attribute under zero conflict, and η 1 0 captures the sensitivity of the salience in ethnic cleavage to I F .
Notice that in our setup, the perceived distance from the own ethnic group
d i , J 2 = 0 for J A , B
because everybody in the own ethnic group shares ethnic attributes and country-wide attributes. Hence I F does not affect i’s utility under ethnic identification. However, it affects i’s utility under national identification. Since the nation consists of members of both ethnic groups A and B in equal parts,8 q N e = 1 2 , and hence q i e q N e 2 = 1 4 for each i. Hence, under national identification,
d i , N 2 = 1 4 w e = 1 4 η 0 + η 1 I F .
Conflict intensity I F depends on the mobilization technology available to the ethnic group as well as each ethnic group’s mobilization resources and depends on the type of foreign intervention as follows:
  • If foreign intervention provides mobilization resources, this affects conflict intensity differently depending on whether or not the foreign intervention is ethnically aligned with the aided group. In the absence of an ethnic alignment, foreign resources do not intensify conflict, so I F = F , with ethnic alignment I F = F + E .
  • If foreign intervention improves mobilization technology, fighting intensity is given by
    I F = α J F J + α J F J .
  • If foreign intervention provides conditional aid, I F = F .
Group status S G is derived from the exogenous intrinsic values of the group σ G 0 and a comparison of the wealth as captured by the net material resources Π G = i G π i of group G A , B , N with respect to the net material resources Π G of reference group G which is either the other ethnic group in the case of ethnic identification or another nation in the case of national identification. Hence,
S G = σ G + Π G Π G
Our equilibrium concept is the social identity equilibrium from Shayo (2009). Formally, we define it as follows.
Definition 1.
A social identity equilibrium is a profile of mobilization efforts ( f i ) i N and a profile of social identities ( g i ) i N such that for all i N , we have f i 0 , y i , g i G i where G i = A , N for i A , and G i = B , N for i B , and
U i ( f i , f i , g i ) U i ( f i , f i , g i ) for   all f i 0 , y i
U i ( f i , f i , g i ) U i ( f i , f i , g i ) for   all g i G i
In other words, the solution concepts require that actions (mobilization efforts) be optimal given current identities and that identities be optimal given current actions. Therefore, our equilibrium analysis can be broken down into two steps. First, we determine optimal mobilization efforts given fixed social identities, i.e., we make sure that our first equilibrium condition (9) holds.9 These efforts serve as candidates for an equilibrium corresponding to the given social identities. Then, we check whether in a social environment associated with a particular pattern of mobilization efforts, the assumed social identities are indeed optimal. In other words, we assess the validity of this candidate equilibrium by examining whether individuals, given the derived mobilization efforts, indeed prefer to maintain the assumed social identity or would rather deviate to an alternative identity. This leads to what we call the no-deviation condition defined by our second equilibrium condition (10). For example, if we derived mobilization efforts under the assumption that all individuals identify nationally, the no-deviation condition for an all-national equilibrium requires that taking the derived mobilization efforts under national identification as given, individual i indeed wants to identify nationally and not deviate to an ethnic identification. Observe that for fixed mobilization efforts, individual i identifies with a nation if and only if
U i ( f i , f i , N ) U i ( f i , f i , J ) for i J = A , B .
Since all individuals in the same ethnic group are assumed to be identical, we follow Sambanis and Shayo (2013) and study symmetric equilibria where all individuals in the same ethnic group choose the same mobilization effort and the same social identification.
In the following sections, we explore various forms of foreign influence that are announced and therefore common knowledge before individuals in the influenced countries decide on their mobilization effort and social identification. We focus on interior solutions to the mobilization efforts where both ethnic groups dedicate a positive amount of resources but less than their entire income to the contest.10 Rather than modeling the decision-making process of foreign influencers, we examine the impact of these different interventions on both conflict and social identity. In particular, we examine whether these interventions increase or decrease the likelihood of an all-ethnic (or, respectively, all-national) equilibrium where all individuals identify ethnically (or, respectively, as a nation). We show that overall domestic mobilization efforts and the intensity of interethnic conflict are higher under ethnic identification than under national identification for all intervention forms we analyze. This tends to translate into lower material payoffs of the intervened country under ethnic identification than under national identification since mobilization efforts are wasted in the control over V.

4. Foreign Influence Through the Contest Success Function

In this section, we examine foreign interventions that affect the competition for control over V. A prominent example includes military interventions, such as the provision of fighting resources or the enhancement in combat capabilities through improved technology. Another example is election interventions: when V denotes the value of political dominance, foreign actors may intervene in the electoral process by supplying either material resources or technological support, thereby influencing the balance of power between competing groups. To disentangle the specific impact of each form of intervention, we analyze the provision of material resources separately from the provision of technological support. Furthermore, we distinguish between unilateral interventions—where foreign support is directed exclusively toward group A—and bilateral interventions, in which foreign actors support both groups within the target country. This approach allows us to systematically assess the strategic and distributive consequences of different intervention configurations.11

4.1. Foreign Provision of Mobilization Resources

We start our analysis with the case where one foreign power provides mobilization resources E A in favor of group A. With this intervention, the material utility function of i A is given by
π i A ( f i ; f i ) = y i f i + F A + E A F + E A V for i A .
On the other hand, the material utility function of an individual i B is given by
π i B ( f i ; f i ) = y i f i + F B F + E A V for i B .
We now introduce the corresponding material payoffs into the individual utility function (1) to derive individual utility under different social identifications and calculate the optimal mobilization efforts for fixed social identifications.
Under ethnic identification, the utility of individual i A is given by
y i f i + F A + E A F + E A V + γ σ A + Y A F A + F A + E A F + E A V Y B F B + F B F + E A V
while the utility of i B is
y i f i + F B F + E A V + γ σ B + Y B F B + F B F + E A V Y A F A + F A + E A F + E A V
Maximizing (12) and (13) with respect to f i yields
1 + F F A F + E A 2 V + γ 1 + 2 F B F + E A 2 V = 0 for i A
and
1 + F + E A F B F + E A 2 V + γ 1 + F + E A F B F + E A 2 V + F A + E A F + E A 2 V = 0 for i B .
The second-order conditions for a maximum are satisfied, namely
2 F F A F + E A 3 V γ 2 F B F + E A 3 V < 0 for i A
2 F + E A F B F + E A 3 V 2 γ F + E A F B F + E A 3 V + F A + E A F + E A 3 V < 0 for i B .
The first-order conditions under ethnic identification can be rearranged as follows.
F + E A 2 = 1 + 2 γ 1 + γ F B V for i A
F + E A 2 = 1 + 2 γ 1 + γ F A + E A V for i B .
Under national identification, individual utility depends on conflict intensity I F which in turn depends on whether or not foreign power is ethnically aligned with the aided group. In the absence of ethnic alignment, the utility of i A is
y i f i + F A + E A F + E A V β η 0 + η 1 F 4 + γ σ N + Y F + V Π N ,
while the utility of i B is given by
y i f i + F B F + E A V β η 0 + η 1 F 4 + γ σ N + Y F + V Π N .
If foreign power is ethnically aligned with the aided group, the term β η 0 + η 1 F 4 in expressions (16) and (17) becomes β η 0 + η 1 F + E A 4 . Notice that this modification will not affect the first-order conditions for individual mobilization efforts under national identification, which are
1 + F F A F + E A 2 V β η 1 4 γ = 0 for i A
1 + F + F F A F B F + E A 2 V β η 1 4 γ = 0 for i B .
Second-order conditions for the maximum clearly hold.12 The first-order conditions for national identification can be rewritten as
F + E A 2 = F B V 1 + β η 1 4 + γ for i A
F + E A 2 = F A + E A V 1 + β η 1 4 + γ for i B
We now derive the optimal domestic mobilization efforts that satisfy the first equilibrium condition (10) of a social identity equilibrium and calculate domestic mobilization efforts.
Lemma 1.
Taking as given the social identification, the domestic mobilization efforts if foreign power provides mobilization resources E A < F B A N to group A are as follows13
  • If both groups identify ethnically,
    F A A B = 1 + 2 γ 4 1 + γ V E A F B A B = 1 + 2 γ 4 1 + γ V
  • If both groups identify nationally,
    F A N N = V 4 1 + β η 1 4 + γ E A F B N N = V 4 1 + β η 1 4 + γ
  • If A identifies ethnically and B nationally,
    F A A N = V 1 + β η 1 4 + γ 1 + 2 γ 2 1 + β η 1 4 + γ 1 + 2 γ + 1 + γ 2 E A F B A N = V 1 + γ 1 + 2 γ 1 + β η 1 4 + γ 1 + 2 γ + 1 + γ 2
  • If A identifies as a nation and B ethnically,
    F A N B = 1 + 2 γ V 1 + γ 1 + 2 γ 1 + β η 1 4 + γ + 1 + γ 2 E A F B N B = V 1 + 2 γ 2 1 + β η 1 4 + γ 1 + 2 γ 1 + β η 1 4 + γ + 1 + γ 2
Proof. 
To calculate the domestic group mobilization efforts, we combined the corresponding first-order conditions. Under all-ethnic identification, we combined (14) and (15). Under national identification, we combined (18) and (19). If A identifies ethnically and B nationally, we combine (14) and (19). If A identifies nationally and B ethnically, we combine (18) and (15). Since resources dedicated to mobilization are the lowest when the group identifies nationally and the other group ethnically, the restriction E A < F B A N = E A + F A N A guarantees that members of the aided group always want to provide a positive amount of mobilization resources. □
Simple calculations establish the following results:
Corollary 1.
F N N < F A N = F N B < F A B for a fixed E A .
Corollary 2.
V > F A B + E A > F A N + E A = F N B + E A > F N N + E A , and total mobilization F + E A is independent of the actual mobilization effort provided by foreign E A .
Lemma 2.
No matter which identification individuals choose, F B and F + E A and F A + E A are always independent of E A , while F and F A are always decreasing in E A .
Remark 1.
Observe that with this particular contest success function, E A serves as a perfect substitute to group A’s domestic mobilization resources. With a different contest success function, it would still be a substitute but not necessarily a perfect substitute; hence the mobilization efforts of the aided group would still be decreasing in the provision of foreign mobilization resources but by less than in the current setting, and total mobilization would depend on E A .
To check whether the mobilization efforts of Lemma 1 are indeed part of a social identity equilibrium, we need to check whether the second equilibrium condition we refer to as the no-deviation condition (10) holds, i.e., whether given the group identification of everybody else and the mobilization efforts, an individual indeed wants to choose the prescribed social identity.
Observe that ethnic identification is better than national identification for individual i if and only if U i ( f i , f i , N ) U i ( f i , f i , J ) for i J = A , B , i.e., when condition (11) is violated. U i ( f i , f i , J ) is given by (12) for i A and by (13) for i B . The utility under national identification U i ( f i , f i , N ) depends on whether foreign mobilization resources increase ethnic salience because of ethnic alignment or not. If not, then U i ( f i , f i , N ) is given by (16) i A and by (17) for i B . Recall, that with ethnic alignment, foreign mobilization efforts intensify ethnic salience, so the term β η 0 + η 1 F 4 in expressions (16) and (17) becomes β η 0 + η 1 F + E A 4 . Introducing these utilities in U i ( f i , f i , N ) U i ( f i , f i , J ) , we can derive a general expression when ethnic identification is better than national identification in the present context. We first analyze the case when foreign mobilization resources increase ethnic salience.
If foreign mobilization resources increase ethnic salience, then the condition that ethnic identification is better than national identification for i A simplifies to
γ σ N σ A + 2 Y B 2 F B + V 2 F B F + E A Π N < β η 0 + η 1 F + E A 4
and for i B to
γ σ N σ B + 2 Y A 2 F A + V 2 F A + E A F + E A Π N < β η 0 + η 1 F + E A 4
Using these conditions and applying them to our no-deviation conditions (10) in the present context, we can state the following: (i) An all-ethnic equilibrium exists if conditions (20) and (21) hold for mobilization efforts F A A B and F B A B . (ii) An all-national equilibrium exists if both conditions (20) and (21) are violated for mobilization efforts F A N N and F B N N . (iii) An equilibrium in which group A identifies ethnically and B nationally exists if condition (20) holds and (21) is violated for mobilization efforts F A A N and F B A N . (iv) An equilibrium in which group A identifies nationally and B ethnically exists if condition (20) is violated and (21) holds for mobilization efforts F A N B and F B N B . We are now in a position to determine how E A affects the existence of these equilibria by examining how it affects conditions (20) and (21). As in Sambanis and Shayo (2013), multiple equilibria can exist for certain parameters.14
By Lemma 2—when foreign mobilization resources influence ethnic salience—group A’s identification can never by affected by a change in E A because both sides of condition (20) are unaffected by a change in E A in all of four candidate equilibria. On the other hand, for group B, condition (21) becomes progressively harder to be satisfied when E A increases because E A reduces F A in all candidate equilibria. In other words, the no-deviation conditions in any candidate equilibrium where B identifies ethnically are tightened, while the no-deviation conditions in any candidate equilibrium where B identifies nationally are relaxed. Observe that relaxing the no-deviation condition for a candidate equilibrium broadens the parameter space in which the equilibrium exists, thereby increasing its likelihood. Conversely, tightening the no-deviation condition narrows the parameter space and makes the equilibrium less likely. We have established the following.
Proposition 1.
When foreign mobilization resources E A increase ethnic salience, providing these resources to group A only will leave A’s incentive to identify ethnically or nationally unaffected but makes the national identification of group B more likely.
For all candidate equilibria, the following holds: (i) E A does not alter F B . (ii) Since E A is a perfect substitute for F A , the more mobilization resources foreign power provides, the fewer domestic mobilization resources provided by group A. (iii) Neither A’s nor B’s probability for obtaining V is affected by E A . This translates into Π A E A > 0 and Π B E A = 0 . Hence, the material payoff of group A increases with E A in any candidate equilibrium, which harms a member of B under ethnic identification (since the reference group becomes richer) but benefits them under national identification (since the nation becomes richer). Both forces make a national identification by group B more likely. It can therefore happen that when both ethnic groups identified ethnically before the intervention, an all-ethnic equilibrium ceases to exist after the intervention, and an equilibrium is reached in which group A identifies ethnically and B nationally, resulting in a further reduction in domestic mobilization since F A N < F A B by Corollary 1.
The Russian election intervention in Moldova’s 2024 EU referendum illustrates an equilibrium outcome where the aided group identifies ethnically and the non-aided group nationally. In this context, ethnic minorities such as the Gagauz, Bulgarians, and Russian-speaking populations—primarily concentrated in regions like Gagauzia and Taraclia—received substantial financial backing from ethnically aligned Russia who shared linguistic and cultural ties. These groups overwhelmingly opposed EU integration (e.g., 95% “No” in Gagauzia and 94% in Taraclia). In contrast, ethnic Moldovans and segments of the Ukrainian minority, who did not receive Russian support, responded to the intervention by strengthening their identification with the Moldovan state. Pre-referendum data from the Ethnobarometer Moldova 2020 showed national identification rates of 80% among Moldovans and 60% among Ukrainians, which rose to 85% and 63%, respectively, after the referendum. Moreover, as predicted by our equilibrium analysis, where F B A N < F A A N + E A , these non-aided groups did not escalate campaign spending (Central Electoral Commission of Moldova, 2024; CIVIS, 2020).
We now return to our model and study the case when foreign power is not ethnically aligned with group A so that foreign mobilization resources do not increase ethnic salience. In this context, ethnic identification is better than national identification for i A if and only if
γ σ N σ A + 2 Y B 2 F B + V 2 F B F + E A Π N < β η 0 + η 1 F 4 .
This inequality (22) constitutes the no-deviation condition for an equilibrium in which i A identifies ethnically, while the violation of (22) constitutes the no-deviation condition for an equilibrium in which i A identifies nationally.
For i B , ethnic identification is better than national identification if and only if
γ σ N σ B + 2 Y A 2 F A + V 2 F A + E A F + E A Π N < β η 0 + η 1 F 4
By Lemma 2, the left-hand side (LHS) of (22) is independent of E A , while the right-hand side (RHS) is decreasing in E A , so ethnic identification becomes progressively more difficult for i A when E A increases, while national identification becomes progressively easier. The no-deviation condition for ethnic identification (22) tightens and the no-deviation condition for national identification relaxes in the respective candidate equilibria. For i B , the no-deviation condition for ethnic identification (23) tightens even further and for national identification relaxes even further when E A increases. This follows immediately from the fact that the LHS of (23) increases in E A , while the RHS decreases. Therefore, we have established the following.
Proposition 2.
When foreign mobilization resources E A do not increase ethnic salience, providing these resources to group A only will make national identification more likely and ethnic identification less likely for both groups.
This stronger result arises because domestic mobilization resources F decline as external support E A increases, which lowers I F and therefore ethnic salience and, in turn, reduces the perceived cost of adopting a national identity.
When a foreign actor provides mobilization resources to group A without sharing its ethnic identity, this intervention tends to make national identification among both groups more likely. If foreign mobilization eliminates an all-ethnic pre-intervention equilibrium and induces a post-intervention all-national equilibrium, this change in equilibrium identification reduces domestic mobilization efforts F beyond the mere substitution effect of foreign resources replacing domestic mobilization effort since F N N < F A B (Corollary 1). Moreover, the intervened country’s material payoff given by
i A π i + i B π i = Y F + V .
increases thanks to the induced identity shift to an all-national identification. Domestic material payoff constitutes a reasonable welfare measure in this context, as the identity-based components of the utility function are inherently subjective and contingent upon personal self-identification.

Two-Sided Provision of Conflict Resources

If both groups receive mobilization resources from foreign interveners, the material payoff to individual i in group J is given by
π i J ( f i ; f i ) = y i f i + F J + E J F + E J + E J V for i J A , B
Introducing this material payoff into the utility functions under ethnic and national identification and maximizing with respect to the mobilization effort allows us to derive the interior candidate equilibria for domestic mobilization efforts given a social identification which satisfies our first equilibrium condition (9). These candidate equilibria can be found in Lemma A1 in Appendix A. We now check how foreign influence affects the no-deviation conditions (10). Observe that the condition (11) for national identification to be preferred to ethnic identification for given mobilization efforts for an individual i belonging to group J becomes
γ σ N σ J + 2 Y J 2 F J + V 2 F J + E J F + E A + E B Π N > β η 0 + η 1 F + E A + E B 4
when foreign mobilization influences ethnic salience and
γ σ N σ J + 2 Y J 2 F J + V 2 F J + E J F + E A + E B Π N > β η 0 + η 1 F 4
when foreign mobilization does not influence ethnic salience. It is obvious from the mobilization efforts derived in Lemma A1 that in all candidate equilibria, F J is decreasing in E J ; similarly, F is decreasing in E J and E J ; moreover, both F J + E J and F + E A + E B are independent of E J and E J . The left-hand side (LHS) of the above inequalities is always increasing when foreign mobilization resources increase, while the right-hand side (RHS) is constant when foreign mobilization affects ethnic salience and is decreasing in foreign mobilization resources when foreign mobilization does not affect ethnic salience. Therefore, the no-deviation condition for ethnic identification tightens, while the no-deviation condition for national identification relaxes.
Proposition 3.
A two-sided intervention through mobilization resources makes ethnic identification less likely and increases the set of parameters of an equilibrium where both groups identify nationally. The effect is stronger when foreign conflict resources do not affect ethnic salience.
Compared to a one-sided provision of conflict resources, a two-sided provision is even more likely to result in an all-national equilibrium. Simple algebra on the mobilization efforts calculated in Lemma A1 reveal that domestic and overall mobilization resources are the lowest in an all-national equilibrium, and hence the overall material payoff for the country Y F + V is the highest. However, it is important to realize that all the results of the present subsection rely on the assumption that the aided group could already achieve its desired level of mobilization without external support. If, instead, the group lacked sufficient resources—so that, in the absence of foreign assistance, its members devoted their entire income to mobilization yet still wished to contribute more—then foreign intervention would raise overall mobilization and could increase the likelihood of ethnic identification, which becomes more salient as mobilization intensifies. In short, the aided group cannot be too resource-constrained for external mobilization support to generate a de-escalatory effect on conflict and a positive effect on material well-being.

4.2. Foreign Influence Through Conflict Technology

Instead of supplying additional mobilization resources, a foreign actor may intervene by enhancing the contest technology, for example, through training, organizational improvements, or advanced equipment. In electoral contexts, this corresponds to interventions that increase the productivity of existing resources—such as improving media strategies, providing superior organizational methods, or granting access to innovative technologies that raise campaign efficiency. As shown below, this type of intervention produces remarkedly different outcomes compared to resource provision, particularly when both groups receive external support and gain equal access to the improved technology. We first examine equilibrium outcomes under conditions of technological symmetry, followed by an analysis of unilateral technological improvements. Together, the analysis also informs us about the effects of asymmetrical technological improvements, which can be analyzed in two steps. First, we introduce a baseline equalization, wherein both groups enhance their conflict technology to a shared minimum threshold. This represents a symmetric improvement from a previously disadvantaged position and is the focus of Section 4.2.1. Second, consider an asymmetric enhancement, in which only one group receives an additional technological advantage, which is analyzed in Section 4.2.2.

4.2.1. Symmetric Technological Enhancements

A technological enhancement in contest technology affects both the contest success function p i J defined in (4) and the intensity of interethnic conflict I F given by (7).15 When the enhancement is symmetric α J = α J > 1 , the contest success function remains unchanged. However, a symmetric enhancement still increases the intensity of interethnic conflict, which lowers the utility from national identification while leaving the utility from ethnic identification unaffected.
Proposition 4.
A symmetric improvement in contest technology for both groups makes an all-ethnic equilibrium more likely and reduces the likelihood of an all-national equilibrium. Concerning equilibria where one group identifies ethnically and the other group nationally, the no-deviation condition of the group that identifies ethnically relaxes. The effect on the no-deviation condition for the nationally identifying group depends on the importance of status. It tightens (softens) when status concerns are relatively weak (strong).
Proof. 
See Appendix B. □
When both groups identify ethnically, the resources allocated to mobilization are unaffected by the effectiveness of the contest technology, represented by α . However, the intensity of intergroup competition I F rises with α , which makes ethnic identification more attractive by increasing the perceived cost of national identification through greater in-group differentiation. This effect explains why, under an all-national identification, mobilization resources decline as α increases—a force that would normally favor national identification—yet the rise in conflict intensity works in the opposite direction. Because the ethnic salience effect dominates the income effect, an all-national equilibrium becomes less likely as α grows. In other words, this type of foreign intervention may eliminate any pre-intervention all-national equilibrium, thereby escalating conflict and reducing the total material payoff of the intervened country Y F + V .16 For candidate equilibria where one group identifies ethnically and the other nationally, the intervention always relaxes the no-deviation condition of the group identifying ethnically. This may lead to a violation of the no-deviation condition for the nationally identifying group, since a higher α amplifies ethnic salience and thus the perceived cost of national identification.
The effects on the total material payoff of the intervened country depend on whether the intervention leads to a violation of the no-deviation conditions and hence eliminates equilibria that existed before the intervention, which can only happen when at least one group identified nationally before the intervention. If a pre-intervention all-national equilibrium or an equilibrium in which one group identifies nationally and the other ethnically survives the intervention, then the intervention actually lowers mobilization since both F N N and F A N = F N B are decreasing in α (see Corollary A2 in Appendix B). However, if the intervention leads to the violation of the no-deviation condition and the group identifies ethnically in the new equilibrium, overall mobilization increases (see Corollary A1 in Appendix B), resulting in a lower overall material payoff. Observe that no matter which equilibrium results after the intervention, fighting intensity I F always increases in α (Corollary A2). Moreover, the higher the α , the more likely it is that the no-deviation condition (10) leads to ethnic identification.
Bosnia and Herzegovina’s 1996 elections and Iraq’s 2005 elections illustrate that when rival foreign sponsors provide comparable technological and organizational enhancements to their respective ethnic or sectarian allies, individuals in the intervened country tend to identify ethnically. In Bosnia’s post-Dayton elections, cross-border logistical support—such as refugee busing and registration engineering—enabled Serb and Croat nationalist parties to convert resources into votes with high efficiency, while Bosniak parties benefited from international assistance in entity-level mobilization; the outcome entrenched ethnic partition in electoral behavior (International Crisis Group, 1996; Schmeets & Exel, 1997). Similarly, Iraq’s 2005 electoral cycle saw Iranian-backed Shi’a parties leverage clerical networks and organizational capacity to achieve bloc discipline, while Kurdish and Sunni lists received targeted external support; this dynamic produced voting patterns overwhelmingly aligned with sectarian identity (Dawisha & Diamond, 2006; Hiltermann, 2006). Across these cases, symmetrically enhanced mobilization technologies—whether through logistics, elite coordination, or media—increased the marginal returns to ethnic appeals, thereby reducing incentives for cross-cutting, national identification.

4.2.2. One-Sided Technological Improvement

Assume now that foreign power provides a better conflict technology to group A only so that the return from its mobilization effort is given by α F A with α > 1 . This distorts the contest success function in favor of group A and therefore influences the material payoffs of the different subgroups as follows:
π i A ( f i ; f i ) = y i f i + α F A α F A + F B V for i A π i B ( f i ; f i ) = y i f i + F B α F A + F B V for i B
while the intensity of interethnic conflict becomes I F = α F A + F B . We solve for the different candidate equilibria (Lemma A3) in Appendix C. Checking how a change in α affects the no-deviation conditions that, given the mobilization efforts, nobody wants to deviate to a different social identity yields the following result.
Proposition 5.
An increase in α affects equilibrium outcomes as follows.17
1. 
In an all-national candidate equilibrium, it tightens the no-deviation condition of group A and softens the no-deviation condition of group B.
2. 
In a candidate equilibrium where group A identifies ethnically and B nationally, the no-deviation condition of group A relaxes. The effect on the no-deviation condition for group B depends on the importance of status. It tightens (softens) when status concerns are relatively weak (strong).
3. 
When the salient weighted ethnic distance term β η 1 exceeds a critical threshold, a rise in α makes the all-ethnic equilibrium more likely. If β η 1 falls below this threshold, group B becomes less likely to identify ethnically in response to sufficiently large technological improvements (i.e., when α increases above a critical threshold). Moreover, when β η 1 is below a lower bound, group B is less likely to identify ethnically for any increase in α.18
Proof. 
See Appendix C. □
Proposition 5 suggests that the most likely equilibrium outcomes due to a technological improvement in group A’s mobilization technology are all-ethnic identification or a situation where A identifies ethnically and B nationally. Which of these equilibria prevails depends on a subtle interaction between γ and β η 1 , the latter capturing the compounded effect of ethnic heterogeneity on the cost of adopting a national identity.
Specifically, β reflects the sensitivity to social or cultural distance between ethnic groups, while η 1 quantifies how interethnic conflict intensifies the perceived salience of these divisions. Together, β η 1 captures the degree to which interethnic conflict and perceived distance jointly exacerbate the challenges of fostering a unified national identity. Not surprisingly, a large β η 1 makes ethnic identification more likely. It is straightforward to show that α F A F B α F A + F B , the difference in the success probabilities of group A with respect to group B in the contest over V, is increasing in α under all social identification profiles. This makes national identification comparatively more advantageous for group B than for group A because the material payoffs of the nation are not contingent on who wins the contest.19 Consequently, the cutoff on β η 1 above which ethnic identification becomes optimal is higher for group B than for group A.
Lebanon’s 2009 parliamentary elections illustrate an asymmetric technological improvement, where one bloc’s superior intervention sharpened ethnic identity, while the rival bloc, with weaker technology, emphasized national inclusivity. Hezbollah and its March 8 allies, backed by Iran and Syria, deployed an advanced information operations infrastructure—centered on Al-Manar television, a sophisticated media ecosystem, and a welfare service network—that dramatically increased the productivity of campaign resources within Shi`a constituencies and reinforced a “resistance” ethnic identity (Clarke, 2017; Lamloum, 2009; Terrorism-Info Center, 2019). In contrast, the Western- and Saudi-supported March 14 coalition lacked comparable embedded networks and instead pursued a civic-national strategy, branding itself as “Lebanon First” and assembling a cross-sectarian alliance of Sunnis, Druze, and Christians (Carter Center, 2009; CFR, 2009; National Democratic Institute, 2009).
Observe that the effects of a one-sided technological improvement in mobilization technology are more nuanced than those of a symmetric two-sided technological improvement. This happens because the latter only affects the overall conflict intensity I F , while the former also alters the contest success function. In both cases, overall conflict intensity I F always increases with α , and mobilization resources are lower under an all-national identification than under an all-ethnic identification.20 Therefore, if the intervention destroys a pre-intervention all-national equilibrium, then conflict is intensified, and the overall material payoff of the intervened nation is reduced.

5. Foreign Power Provides Conditional Aid

Foreign actors may not become directly involved in the competition over the resource V, but they may offer conditional aid of magnitude Δ . We will assume that Δ is considerably smaller than V to ensure 0 < f i < y i for all individuals.21 The provision of this aid can be contingent upon the control of V by group A, in which case we distinguish two scenarios.
(i)
Universal Benefit: Aid is distributed broadly and benefits all individuals. Aid is non-exclusive.
(ii)
Exclusive Benefit: Aid is allocated solely to members of group A.
Alternatively, the provision of aid might be contingent on specific forms of social identification, such as ethnic or national affiliation.
We now proceed to analyze the implications and dynamics of these scenarios in greater detail.

5.1. Universal Aid Conditional on Group A Controlling V

We examine a situation where aid is conditional on the governance of group A but is not limited to its members. For example, foreign direct investment (FDI) may flow only when group A governs, yet its economic benefits, such as job creation and infrastructure development, are broadly shared across society. Similarly, post-conflict reconstruction assistance may be tied to the leadership of group A, while improvements in public services, housing, and transportation ultimately benefit the entire population. Non-exclusive aid affects the material payoff as follows:
π i = y i f i + F A F V + Δ for i A π i = y i f i + F B F V + F A F Δ for i B
While the payoff from status under ethnic identification is unaffected by Δ , status increases under national identification since both groups enjoy Δ if group A controls V. Hence, under ethnic identification, group A only benefits from Δ through the increase in material payoff, while under national identification, the material payoff and the payoff from status increase. If group B loses the contest, it still benefits from Δ , so the cost of losing is substantially reduced. We will assume that V > Δ 1 + 2 γ which, as shown in Appendix D, ensures that individuals in group B still want to mobilize and do not simply prefer yielding power to A.
Proposition 6.
Foreign power providing universal inclusive aid conditional on group A controlling V makes an all-ethnic equilibrium less likely and an all-national equilibrium more likely by relaxing the no-deviation condition for an all-national equilibrium for group B.
Proof. 
See Appendix D. □
Since both groups benefit from aid under the same conditions, the provision of universal aid does not alter the relative material payoffs between in-group and out-group conditions under ethnic identification, but it substantially raises the material payoff from national identification. This effect is particularly strong for group B, as it can only obtain access to aid if group A wins control of V.
Proposition 6 predicts that non-exclusive conditional aid contingent on one group’s control of V is likely to result in an all-national equilibrium. This reduces the amount of resources dedicated to mobilization since F N N < F A B (Corollary A5 in Appendix D). Observe that the material wealth of group A is given by Y A F A + F A F V + Δ and the material wealth of group B by Y B F B + F B F V + F A F Δ , so the total material wealth in the intervened country is
Y F + V + 2 F A F Δ .
Under all-ethnic identification,
2 F A A B F A B Δ = V + Δ + 2 V γ V 1 + 2 γ Δ ,
and under all-national identification,
2 F A N N F N N Δ = V + Δ + 2 Δ γ V Δ .
Simple calculations show that
2 F A N N F N N Δ 2 F A A B F A B Δ = 4 V Δ 2 γ γ + 1 2 γ + 1 > 0 .
Since F A N N < F A A B , the material payoff of the entire country is always higher under an all-national identification than under an all-ethnic identification. Hence, inclusive development programs result in the highest material payoff if they lead to national identification, which is the most likely outcome.
Proposition 6 aligns with evidence from randomized evaluations of inclusive development programs. In Afghanistan, the National Solidarity Program—implemented with donor conditionality on community participation—significantly improved pro-government attitudes and reduced insurgent violence in relatively secure districts, consistent with a shift toward civic-national frames (Beath et al., 2025). Similarly, in Iraq, localized U.S. aid projects (CERP) reduced insurgent attacks, particularly when implementation credibility was high, suggesting that inclusive aid can strengthen identification with the state rather than ethnic blocs (Berman et al., 2011). At the macro level, EU accession conditionality on minority rights demonstrates that credible, inclusive conditionality can reorient elite strategies toward civic integration (Rechel, 2009; Vachudova, 2005).

5.2. Exclusive Conditional Aid

We now examine a situation where aid is conditional on group A controlling V and exclusively enjoyed by group A. For example, targeted economic aid—such as grants for business development, agricultural subsidies, or preferential trade agreements—may be directed solely toward regions or sectors dominated by group A. In some cases, international scholarships or educational exchanges are restricted to individuals affiliated with group A. Another example includes humanitarian aid distributed through government-controlled channels that systematically favor group A’s constituencies, leaving others underserved.
With exclusive aid, the material payoff of i A remains as specified by (25), while the material payoff of i B is unaffected by aid. Consequently, receiving aid raises the ethnic status of group A and lowers that of group B. However, because aid is conditional on A controlling V, group B’s incentive to allocate resources to mobilization increases as this mitigates the status loss from one-sided aid. When V is sufficiently high, exclusive aid always relaxes the no-deviation conditions of all-ethnic identification.
Proposition 7.
Sufficient conditions for an increase in Δ to increase the range of parameters for which an all-ethnic equilibrium exists are given by V > max 2 Δ , γ Δ , 1 .
Proof. 
See Appendix E. □
In other words, an all-ethnic equilibrium becomes more likely, leading to more mobilization resources ( F A B > F N N Corollary A6 in Appendix E).
With exclusive conditional aid, the total material payoff of the intervened country is given by
Y F + V + F A F Δ .
Introducing the corresponding mobilization efforts, under all-ethnic identification,
F A A B F A B = V 1 + 2 γ + Δ 1 + γ 2 V + Δ 1 + 2 γ
while under all-national identification,
F A N N F N N = V + 1 + γ Δ 2 V + Δ
Simple calculus reveals that F A A B F A B < F A N N F N N , so material welfare is higher under national identification, but the intervention is likely to lead to ethnic identification.
The statement that exclusive conditional aid to group A is likely to result in all-ethnic equilibria is corroborated by studies of ethnic favoritism in Africa. Jablonski (2014) shows that Kenyan incumbents systematically channel donor-funded projects to coethnic regions, increasing electoral returns and reinforcing ethnic mobilization. Cross-national evidence further indicates that foreign aid inflows amplify regional favoritism in weak institutional environments (Hodler & Raschky, 2014), while geocoded analyses of Chinese development finance reveal strong targeting to leaders’ home regions (Dreher et al., 2019). These patterns confirm that exclusive aid conditionality heightens the material and status payoffs of ethnic identification.

5.3. Aid Conditional on Social Identification

Aid conditional on social identification refers to external assistance that is allocated based on ethnic or national identification. While we assume that aid conditional on ethnic identification requires group A to control V, aid conditional on national identification may or may not be contingent on group A controlling V. Conditioning aid on social identification might serve as a focal point in situations where multiple social identity equilibria co-exist and thereby serve as an equilibrium selection device. Our analysis abstracts from this and considers how individual incentives are affected by these interventions, i.e., we study which equilibria exist after these interventions are announced.22

5.3.1. Aid Conditional on Ethnic Identification of A

Foreign aid Δ conditional on both ethnic identification and political control refers to assistance that is provided exclusively to members of a specific ethnic group and only when that group holds control over the strategic resource or territory denoted by V. For example, a foreign government may offer development aid, military support, or cultural funding only when group A governs and only to individuals or institutions that explicitly identify as part of that ethnic group. In such cases, individuals who identify primarily with a broader national identity, or who advocate for civic inclusion, may be excluded from the aid’s benefits.
Proposition 8.
If aid is conditional on group A controlling V and ethnic self-identification, a sufficient condition for an all-ethnic equilibrium to become more likely when Δ increases is that V > max Δ 2 , 1 . The no-deviation condition for an all-national identity equilibrium is unaffected by Δ for group B. The same holds for group A if a unilateral deviation to ethnic identification does not give access to aid. Otherwise, the no-deviation condition for an all-national identity equilibrium tightens for group A when Δ increases.
Proof. 
See Appendix F. □
The all-ethnic candidate equilibrium is identical to the case of unilateral aid when A receives aid in the case of controlling V. So is the no-deviation condition for this equilibrium for i B , since aid will still be received by all individuals in group A when i B deviates to national identification. However, the no-deviation condition of i A changes. The deviating member will no longer receive aid, which reduces this member’s material payoff, but all other members of group A still receive aid since they continue to identify ethnically.23
Under national identification, no individual receives aid; thus, mobilization efforts are unaffected by aid. A deviation to ethnic identity by any i B does not confer aid to the deviator. For i A , the attractiveness of a unilateral deviation hinges on whether aid becomes accessible under the deviation. If aid remains unavailable, the no-deviation condition is unchanged; if aid is granted, the incentive to deviate increases with Δ .
Since ethnic identification potentially increases V by Δ for i A , total mobilization resources under ethnic identification are increasing in Δ and are always greater than those under national identification (see Corollary A7 in Appendix F). Consequently, since the intervention makes an all-ethnic equilibrium more likely, the intervention is likely to increase mobilization. The impact on the intervened country’s aggregate material payoff depends on the size of Δ , which is only granted to group A under ethnic identification and when in control of V. Under an all-ethnic identification, aggregate material payoff is Y F A B + V + F A A B F A B Δ and is strictly increasing in Δ .24 In contrast, total material payoff in an all-national equilibrium is given by Y F N N + V and is independent of Δ . Therefore, for sufficiently high Δ , ethnic identification may yield a higher aggregate material payoff.
Proposition 8, which predicts that aid conditional on both political control and ethnic identification is likely to result in all-ethnic equilibria, is consistent with micro-level evidence that Chinese aid projects increase ethnic identity salience among African respondents (Isaksson, 2020). This effect is absent for Western donors, underscoring the role of identity-gated conditionality in shaping social identification.

5.3.2. Aid Conditional on National Identification

In situations where foreign aid is conditional on national identification, individuals or groups who identify primarily along ethnic lines may be excluded either directly or indirectly. This exclusion often arises through eligibility criteria that require recipients to demonstrate allegiance to a unified national identity, civic values, or participation in state-led initiatives promoting national cohesion. Ethnic communities that resist these narratives or maintain separate institutions may be left out. For example, a foreign-funded civic education program might only be implemented in schools that adopt a national curriculum emphasizing unity and shared history, thereby excluding ethnic schools with distinct educational systems. Furthermore, aid may support cultural initiatives that promote national symbols, language, and identity while ignoring or marginalizing ethnic traditions. Foreign donors might fund national museums or media campaigns celebrating civic unity while declining to support ethnic cultural centers or minority-language media. Finally, foreign donors might provide aid to construct a unified army or an inclusive state which is only valued by people who identify nationally. This aid could be unconditional on who controls V but could also be conditional on group A’s governance, especially in cases where foreign power is more aligned with group A and trust or controls group A to implement the required measures, while this cannot be ensured if group B is in power.
We start analyzing the case where aid is conditional on national identification independently of who controls V. Since the reception of aid only depends on national identification, it does not affect mobilization efforts. Aid increases the attractiveness of national identification, leaves the utility of ethnic identification unaltered if both groups identify ethnically, and reduces the utility of ethnic identification if the other group identifies nationally and therefore receives aid. This immediately implies the following:
Proposition 9.
Aid conditional on national identification independently of who controls V reduces the likelihood of ethnic identification and increases the likelihood of an all-national equilibrium.
We now turn to the scenario when aid is conditional on group A being in control of V and adopting a national identity. Under these conditions, group B receives aid only if it also identifies nationally and group A remains in power with a national identity, not when group A governs with an ethnic identity. Therefore, aid has no effects on the incentives to deviate from an all-ethnic candidate equilibrium for i B . The same holds for i A if being the only person identifying nationally does not give access to aid when A controls V. If only individual national identification is required for the receipt of aid, i A has increased incentives to deviate to national identification since they receive aid under A’s governance.
Proposition 10.
Aid conditional on both national identification and A controlling V makes an all-national equilibrium more likely. It reduces the likelihood of an all-ethnic equilibrium if unilateral deviations to national identification are sufficient for a member of group A to receive aid when A controls V. If a unilateral deviation of i A does not result in the receipt of aid, aid does not change the existence conditions of an all-ethnic equilibrium.
Proof. 
See Appendix G. □
Observe that the mobilization efforts of an all-national candidate equilibrium are identical to the case of bilateral aid. What changes are the no-deviation conditions. An individual deviation to ethnic identification implies that personal access to aid is foregone, which is a bigger sacrifice when Δ rises, while everybody else who is not deviating still obtains access to aid. In Appendix G, we derive the no-deviation conditions for an all-national equilibrium candidate as follows:
F A N N F N N Δ + γ σ N σ A + 2 Y B 2 F B N N + 2 F B N N F N N V + 2 F A N N F N N Δ Π N > β η 0 + η 1 F N N 4
for i A , and
F A N N F N N Δ + γ σ N σ B + 2 Y A 2 F A N N + 2 F A N N F N N V + Δ Π N > β η 0 + η 1 F N N 4
for i   B .
The overall domestic resources dedicated to mobilization under national identification F N N decrease when Δ increases, so the perceived cost of adopting a national identity decreases since ethnic salience is reduced by lower mobilization. Moreover, under national identification, aid receipt by members of the other group is valued positively, while it is valued negatively under ethnic identification. The same applies to the receipt of V by the other group. However, the probability of members of the other group enjoying Δ and V depends on the underlying equilibrium mobilization efforts, and higher mobilization by the other group reduces the attractiveness of national identification. Nevertheless, increases in Δ raise the combined expected gains and losses associated with the other group’s mobilization. Taken together, these forces make an all-national equilibrium more likely as Δ increases.
Since F N N < F A B (Corollary A8 in Appendix G) and V is (potentially) increased by Δ under national identification, the total material payoff of the intervened country is always higher in an all-national equilibrium than in an all-ethnic equilibrium.
The idea that aid conditional on national identification—either universally or contingent on A’s control—makes ethnic equilibria less likely and civic-national alignment more likely finds support in both micro and macro studies. In Afghanistan, civic-framed aid programs improved trust in state institutions (Beath et al., 2025), while EU conditionality on inclusive governance induced elites to adopt national integration policies (Vachudova, 2005). Experimental evidence on donor responses to rights violations further shows that credible conditionality can shift domestic accountability and reduce resistance to nationally framed reforms (Dasandi et al., 2022). Collectively, these findings validate the model’s core claim: the design of aid conditionality—exclusive versus inclusive, ethnic versus civic—systematically shapes the equilibrium between ethnic and national identification.

6. Discussion and Conclusions

This paper demonstrates that foreign influence is not merely a matter of shifting material capabilities but a powerful force in shaping equilibrium social identity and conflict intensity. Our model reveals that the nature and design of foreign interventions can make either ethnic divisions or a civic-national alignment more likely. We show that under ethnic identification, mobilization efforts are higher than under national identification. Since these mobilization efforts are only a means to achieving V (which might be augmented by aid), the material payoff of the intervened nation is typically lower under an all-ethnic than all-national identification.
Our findings carry significant implications for foreign policy and peacebuilding. Upgrades of mobilization technology and exclusive or ethnically targeted aid increase the likelihood of an all-ethnic equilibrium outcome, thereby increasing domestic mobilization resources. In contrast, inclusive aid and aid conditional on national identification are more likely to reduce conflict and promote national identification. The same applies to the provision of mobilization resources, as long as these resources were not needed to achieve the desired group mobilization effort in the absence of the intervention. If the group lacked sufficient resources (was too poor) to mobilize up to their desired level, foreign resources will increase overall conflict.
We can easily obtain further insights by applying some of the results derived in Sambanis and Shayo (2013) to the context of foreign interventions. A foreign intervention might affect group status σ J or national status σ N , making either ethnic or national identification more likely. Increasing σ J or lowering σ N makes ethnic identification more likely and national identification less likely.25 Similarly, by intervening in favor of one ethnic group, foreign intervention might increase the salience of the ethnic attribute unrelated to conflict η 0 , making ethnic identification coupled with high-intensity conflict mobilization more likely.26 If foreign power is the reference group for national identification, the intervention itself might affect foreign national income Π N , which favors national identification if Π N decreases due to the resources invested in the intervention, but it makes ethnic identification more likely if Π N increases if foreign power benefits sufficiently from the intervention and leaves the aided “nation” comparatively worse off ( Π N Π N decreases).
A further possibility is that the foreign intervention can convert the external actor into the aided group’s reference group. If the foreign actor’s income differs substantially from that of the group it replaces as a reference, this alone can influence whether individuals favor civic or ethnic identification in the affected country. Additionally, some members of the aided group may feel closer to the foreign actor, creating intragroup divisions between core members aligned with the foreign power and others who are closer to the nation than the foreign actor. As shown in Sambanis and Shayo (2013), such divisions can lead to different identification choices among core and non-core members, where, as shown in Lemma 2 in Sambanis and Shayo (2013), core members identify ethnically, but non-core members identify with the nation. Hence, core members desire a higher degree of mobilization than non-core members. The overall conflict intensity depends on whether core members have sufficient resources to sustain their desired high level of mobilization. If foreign intervention increases these mobilization resources, overall conflict intensity will increase.
The above insights underscore the importance of designing foreign interventions with an acute awareness of identity dynamics. Rather than treating identity as an exogenous backdrop, policymakers must recognize it as a central mechanism through which external influence operates.

Funding

Esther Hauk acknowledges financial support from the Severo Ochoa Programme for Centers of Excellence in R&D (Barcelona School of Economics CEX2024-001476-S), funded by MCIN/AEI/10.13039/501100011033 and from the Ministerio de Ciencia e Innovación through research project PID2021-126209OB-I00 funded by MCIN/AEI/10.13039/501100011033 and by ERDF A way of making Europe.

Data Availability Statement

No new data were created or analyzed in this study.

Conflicts of Interest

The author declares no conflicts of interest.

Appendix A. The Two-Sided Provision of Mobilization Resources

If both groups in a country receive foreign mobilization resources, the utility of individual i J who identifies ethnically is given by
y i f i + F J + E J F + E A + E B V + γ σ J + Y J Y J F J + F J + E J F + E A + E B V + F J F J + E J F + E A + E B V
Maximizing with respect to f i leads to the first-order condition
F + E A + E B 2 = F J + E J V 1 + 2 γ 1 + γ .
If foreign power is not ethnically aligned with any of the groups, then under national identification, the utility i J who identifies as a nation is
y i f i + F J + E A + E B F + E A + E B V β η 0 + η 1 F 4 + γ σ N + Y F + V Π N .
If both foreign groups are ethnically aligned, the term β η 0 + η 1 F 4 is substituted by β η 0 + η 1 F + E A + E B 4 . The first-order conditions are not affected by whether the term β η 0 + η 1 F 4 is substituted by β η 0 + η 1 F + E A + E B 4 and are given by
F J + E J 1 + β η 1 4 + γ V = F + E A + E B 2 .
Combining these first-order conditions gives rise to the candidate equilibria described in the following lemma.
Lemma A1.
Foreign mobilization resources are a perfect substitute for domestic mobilization resources so that total mobilization is independent of foreign resources. In the different candidate equilibria, group mobilization efforts are as follows:
  • If both groups identify ethnically,
    F B A B + E B = F A A B + E A = V 1 + 2 γ 4 1 + γ
  • If both groups identify nationally,
    F B N N + E B = F A N N + E A = V 4 1 + β η 1 4 + γ
  • If A identifies ethnically and B nationally, then
    F A A N + E A = V 1 + 2 γ 2 1 + β η 1 4 + γ 1 + γ 2 1 + 1 + 2 γ 1 + γ 1 + β η 1 4 + γ 2 F B A N + E B = V 1 + 2 γ 1 + γ 2 1 + γ 2 + 1 + 2 γ β η 1 4 2
  • If A identifies as a nation and B ethnically,
    F A N B + E A = V 1 + 2 γ 1 + γ 2 1 + γ 2 + 1 + 2 γ β η 1 4 2 F B N B + E B = V 1 + 2 γ 2 1 + β η 1 4 + γ 1 + γ 2 1 + 1 + 2 γ 1 + γ 1 + β η 1 4 + γ 2
Since resources devoted to group mobilization in favor of group J are the lowest under F J N J + E J , a sufficient condition for interior mobilization efforts by both groups is that E J < V 1 + 2 γ 1 + γ 2 1 + γ 2 + 1 + 2 γ β η 1 4 2 .

Appendix B. Symmetric Improvement in Mobilization Technologies

In this appendix, we prove Proposition 4. As usual, we proceed in two steps. We first derive the candidate equilibria for mobilization efforts satisfying our first equilibrium condition (9) and then check how the intervention affects the no-deviation condition (10).
Under symmetric improvements in mobilization technologies due to foreign interventions, an individual i J who identifies nationally chooses f i to maximize
y i f i + α F J α F A + α F B V β η 0 + η 1 α F J + F J 4 + γ σ N + Y F + V Π N
while an individual i J who identifies ethnically chooses f i to maximize
y i f i + α F J α F A + α F B V + γ σ J + Π J Π J = y i f i + F J F J + F J V + γ σ J + Y J Y J F J F J + F J F J F J + F J V
which turns out to be identical to the ethnic identification in Sambanis and Shayo (2013).
The first-order conditions for mobilization efforts are
F 2 1 + γ + β η 1 α 4 = F J V
under national identification and
F 2 = F J V 1 + 2 γ 1 + γ
under ethnic identification. By combining these conditions, we obtain Lemma A2.
Lemma A2.
The domestic mobilization efforts of different ethnic subgroups, assuming both receive improved mobilization technology and taking as given the group identification, are as follows:
  • If both subgroups identify ethnically,
    F A A B = F B A B = 1 + 2 γ 1 + γ V 4
  • If both subgroups identify nationally,
    F J N N = V 4 1 + γ + β η 1 α 4 for J A , B
  • If subgroup J identifies as a nation and subgroup J identifies ethnically, then
    F J = 1 + 2 γ 1 + γ 1 + 2 γ 1 + γ + β η 1 α 4 + 1 + γ 2 V
    F J = 1 + 2 γ 2 1 + γ + β η 1 α 4 1 + 2 γ 1 + γ + β η 1 α 4 + 1 + γ 2 V
Simple calculus reveals that
Corollary A1.
V > F A B > F A N = F N B > F N N .
Corollary A2.
F A B α = 0 , and F A N α = F N B α < 0 , and F N N α < 0 , but fighting intensity I F is always increasing in α.
We now examine how the foreign intervention affects the no-deviation conditions (10) for each equilibrium candidate. Given the above mobilization efforts, identifying as a nation is better than identifying ethnically for group i J if and only if (A1) > (A2) or equivalently
β η 0 + η 1 α F 4 + γ σ N + 2 Y J 2 F J + V Π N > γ σ J + F J F J F V
For an all-ethnic equilibrium to hold, condition (A5) needs to be violated. The no-deviation condition for each i J therefore becomes
γ σ N σ J + 2 Y J 2 F J A B + V Π N < β η 0 + η 1 α F A B 4
Both F J A B and F A B are independent of α , so the left-hand side (LHS) of (A6) does not change with α , but its right-hand side (RHS) increases in α . So when α increases, an all-ethnic equilibrium is more likely to be reached.
Both groups identifying nationally is the best response when (A5) holds, and therefore the no-deviation condition for each i J becomes
γ σ N + 2 Y J 2 F J N N + V Π N > β η 0 + η 1 α F N N 4
Simple calculations show that F J N N is decreasing in α , and α F N N is increasing in α , so both sides of (A7) are increasing in α . To assess the overall effect, we move all terms of (A7) to the LHS and introduce F N N and F J N N into the condition, which becomes
β η 0 + η 1 V α 2 1 + γ + β η 1 α 4 4 + γ σ N + 2 Y J V 2 1 + γ + β η 1 α 4 + V Π N > 0 .
Calculating the derivative of the LHS with respect to α , we get
V β η 1 4 2 1 + γ + β η 1 α 4 2 < 0 .
Hence, the LHS decreases in α , which implies that an all-national identification becomes more difficult (less likely) when α increases.
For the case where one group identifies nationally and the other ethnically, we assume without loss of generality that A identifies nationally and B ethnically (the opposite case follows by symmetry). The no-deviation condition for i B requires that ethnic identification is better than national identification. Therefore,
γ σ B + F B N B F A N B F N B V + β η 0 + η 1 α F N B 4 γ σ N + 2 Y A 2 F A N B + V Π N > 0
The first and the second summands of the LHS are increasing in α , but the third is decreasing in α . 27 Taking the derivative of the entire LHS with respect to α , we get
8 β η 1 γ + 1 2 γ + 1 2 8 γ + 8 γ 2 + α β η 1 + 2 α β γ η 1 + 8 16 γ + 8 γ 2 + α β η 1 + 2 α β γ η 1 + 8 3 V > 0
so ethnic identification for B becomes more likely when α increases.
The no-deviation condition for i A to prefer national identification to ethnic identification when B identifies ethnically becomes
β η 0 + η 1 α F N B 4 + γ σ N σ A + 2 Y B 2 F N B + F B N B F A N B F N B V + V Π N > 0
Now it is the first term of the sum that is decreasing in α , while the second is increasing in α . 28 The derivative of the LHS with respect to α is given by
8 β η 1 2 γ + 1 16 γ + 8 γ 2 + α β η 1 + 2 α β γ η 1 + 8 3 * V 24 γ + 16 γ 2 16 γ 3 16 γ 4 + α β η 1 2 α β γ 2 η 1 4 α β γ 3 η 1 + 2 α β γ η 1 + 8
The sign of the derivative can go in both directions depending on the sign of the expression in the bracket of the second line. If this expression is positive, then the sign of the entire expression is negative, and the condition becomes more difficult to be satisfied. A sufficient condition for this to happen is that γ < 1 2 2 because for this value, α β η 1 2 α β γ 2 η 1 4 α β γ 3 η 1 + 2 α β γ η 1 > 0 . Hence for low values of γ (i.e., status does not matter much), national identification for group A when B identifies ethnically becomes more difficult, but when status matters a lot, the opposite holds. It is easy to see that for sufficiently high values of γ , the sign of the derivative becomes positive, and hence the condition is easier to be satisfied.

Appendix C. One-Sided Technological Improvement

Assume that only group A’s mobilization technology is improved by α > 1 . We start by calculating the mobilization efforts that satisfy equilibrium condition (9). In this case, under ethnic identification, an individual i belong to group A chooses f i to maximize
y i f i + α F A α F A + F B V + γ σ A + Y A F A + α F A α F A + F B V Y B F B + F B α F A + F B V
while an individual i belonging to group B who identifies ethnically maximizes
y i f i + F B α F A + F B V + γ σ B + Y B F B + F B α F A + F B V Y A F A + α F A α F A + F B V .
The first-order conditions with respect to f i are
α F A + F B 2 = α F B V 1 + 2 γ 1 + γ for i A
α F A + F B 2 = α F A V 1 + 2 γ 1 + γ for i B
On the other hand, under national identification, individual i A maximizes
y i f i + α F A α F A + F B V β η 0 + η 1 α F A + F B 4 + γ σ N + Y F + V Π N
while individual i B maximizes
y i f i + F B α F A + F B V β η 0 + η 1 α F A + F B 4 + γ σ N + Y F + V Π N
resulting in the following first-order conditions with respect to f i :
α F A + F B 2 = α F B V 1 + β η 1 α 4 + γ for i A
α F A + F B 2 = α F A V 1 + β η 1 4 + γ for i B
Combining the corresponding first-order conditions and simple algebra gives
Lemma A3.
The mobilization efforts of the different ethnic subgroups if foreign intervention provides improved mobilization technology to subgroup A, taking as given the group identification, are as follows:
  • If both groups identify ethnically, they choose the same mobilization effort
    F B A B = F A A B = α V 1 + α 2 1 + 2 γ 1 + γ
    leading to
    I A B = α F A A B + F B A B = α V 1 + α 1 + 2 γ 1 + γ
  • If both groups identify nationally, then F B N N > F A N N where
    F A N N = α V 1 + β η 1 4 + γ β η 1 α 2 + 1 + γ 1 + α 2 F B N N = α V 1 + β η 1 α 4 + γ β η 1 α 2 + 1 + γ 1 + α 2
    leading to
    I N N = α F A N N + F B N N = α V β η 1 α 2 + 1 + γ 1 + α
  • If group A identifies ethnically and B nationally and F A A N > F B A N ,
    F A A N = α V 1 + β η 1 4 + γ 1 + 2 γ 2 α 1 + 2 γ 1 + β η 1 4 + γ + 1 + γ 2 F B A N = α V 1 + 2 γ 1 + γ α 1 + 2 γ 1 + β η 1 4 + γ + 1 + γ 2
    leading to
    I A N = α F A A N + F B A N = α V 1 + 2 γ α 1 + 2 γ 1 + β η 1 4 + γ + 1 + γ
  • If group B identifies ethnically and A nationally, then F B N B > F A N B , where
    F A N B = α V 1 + 2 γ 1 + γ α 1 + γ + 1 + β η 1 α 4 + γ 1 + 2 γ 2 F B N B = α V 1 + β η 1 α 4 + γ 1 + 2 γ 2 α 1 + γ + 1 + β η 1 α 4 + γ 1 + 2 γ 2
    leading to
    I N B = α F A N B + F B N B = α V 1 + 2 γ α 1 + γ + 1 + β η 1 α 4 + γ 1 + 2 γ
Simple algebra reveals the following:
Corollary A3.
Fighting intensity is always increasing in α. Moreover, I A B > I N B > I A N > I N N .
Corollary A4.
F A B > F N N , and F A B α < 0 , and F N N α < 0 .
Proof. 
To see this, observe that
F A B = 2 1 + α 2 1 + 2 γ 1 + γ α V
F N N = 1 + β η 1 4 + γ + 1 + 2 γ 1 + γ β η 1 α 2 + 1 + γ 1 + α 2 α V
Simple calculus reveals that F A B α < 0 and F N N α < 0 . Now F A B > F N N is equivalent to
2 1 + 2 γ β η 1 α 2 + 1 + γ 1 + α 2 > 1 + γ 1 + α 2 1 + β η 1 4 + γ + 1 + 2 γ 1 + γ
which can be rewritten as
2 1 + 2 γ β η 1 2 α 2 4 + β η 1 α 1 + γ 1 + α + 1 + γ 2 1 + α 2 > 1 + γ 1 + α 2 β η 1 4 + 2 + 2 γ 1 + γ 2 1 + α 2
and further simplifies to
2 γ 1 + γ 2 1 + α 2 + 1 + 2 γ β η 1 2 α 2 2 + β η 1 1 + γ 1 + α 2 1 + 2 γ α 1 + α 4 > 0
The expression is positive since 2 1 + 2 γ α 1 + α 4 = 7 4 α + 4 α γ 1 4 is always positive when α > 1 . □

Proof of Proposition 5

Identifying as a nation is better than identifying ethnically for i J if and only if condition (11) is satisfied, which, in the present setup, is equivalent to
β η 0 + η 1 α F A + F B 4 + γ σ N + Y 2 F B + V Π N > γ σ A + Y A Y B + α F A F B α F A + F B V
for i A and to
β η 0 + η 1 α F A + F B 4 + γ σ N + Y 2 F A + V Π N > γ σ B + Y B Y A α F A F B α F A + F B V
for i B .
An all-ethnic equilibrium exists, leading to F B A B = F A A B when both conditions (A16) and (A17) are violated. For i A , this requires
β η 0 + η 1 α F A A B + F B A B 4 + γ σ N + Y 2 F B A B + V Π N < γ σ A + Y A Y B + α F A A B F B A B α F A A B + F B A B V
and for i B , the condition is
β η 0 + η 1 α F A A B + F B A B 4 + γ σ N + Y 2 F A A B + V Π N < γ σ B + Y B Y A α F A A B F B A B α F A A B + F B A B V
Lemma A4.
Increasing α, improving the mobilization technology of group A, affects the conditions for the existence of an all-ethnic equilibrium as follows:
  • For β η 1 > 2 γ 2 + 3 γ 1 + 2 γ , both conditions (A18) and (A19) become easier to be satisfied and hence an all-ethnic equilibrium more likely.
  • For 2 γ 2 + 3 γ 1 + 2 γ > β η 1 > 2 γ 1 + γ 1 + 2 γ , condition (A18) for group A becomes easier to be satisfied, but for group B, condition (A19) becomes easier to be satisfied if and only if α < 2 γ 2 + β η 1 1 + 2 γ 4 γ + 6 γ 2 β η 1 1 + 2 γ = 2 γ 2 + β η 1 1 + 2 γ 2 γ 2 + 3 γ β η 1 1 + 2 γ , and it becomes more difficult for group B when α > 2 γ 2 + β η 1 1 + 2 γ 2 γ 2 + 3 γ β η 1 1 + 2 γ .
  • For 2 γ 1 + γ 1 + 2 γ > β η 1 > 2 γ 2 1 + 2 γ , condition (A18) for group A becomes easier to be satisfied, but for group B, condition (A19) is always harder to be satisfied.
  • When β η 1 < 2 γ 2 1 + 2 γ , condition (A18) for group A becomes easier to be satisfied if and only if α < 4 γ + 6 γ 2 + β η 1 + 2 β γ η 1 2 γ 2 β η 1 1 + 2 γ = 2 γ 2 + 3 γ + β η 1 1 + 2 γ 2 γ 2 β η 1 1 + 2 γ and becomes harder otherwise. For group B, condition (A19) is always harder to be satisfied.
Proof. 
We rewrite conditions (A18) and (A19) by collecting terms on one side. For i A , the no-deviation condition for an all-ethnic equilibrium is
0 < β η 0 + η 1 α F A A B + F B A B 4 γ σ N + Y 2 F B A B + V Π N + γ σ A + Y A Y B + α F A A B F B A B α F A A B + F B A B V
Now we calculate the derivative of the RHS with respect to α .
V α + 1 3 γ + 1 4 γ + 6 γ 2 + β η 1 2 α γ 2 + α β η 1 + 2 β γ η 1 + 2 α β γ η 1
If the derivative is positive, condition (A18) is relaxed, while it tightens if the derivative is negative. The derivative is positive for 4 γ + 6 γ 2 + β η 1 + 2 β γ η 1 > α 2 γ 2 β η 1 1 + 2 γ , which is always true for 2 γ 2 β η 1 1 + 2 γ < 0 or equivalently β η 1 > 2 γ 2 1 + 2 γ . If β η 1 < 2 γ 2 1 + 2 γ , then the condition is positive for α < 4 γ + 6 γ 2 + β η 1 + 2 β γ η 1 2 γ 2 β η 1 1 + 2 γ = 2 γ 2 + 3 γ + β η 1 1 + 2 γ 2 γ 2 β η 1 1 + 2 γ .
Similarly, we rewrite condition (A19) for i B as
0 < β η 0 + η 1 α F A A B + F B A B 4 γ σ N + Y 2 F A A B + V Π N + γ σ B + Y B Y A α F A A B F B A B α F A A B + F B A B V
and calculate the derivative of the RHS with respect to α
β η 1 V 1 + 2 γ 1 + γ 1 1 + α 2 + 2 γ V 1 + 2 γ 1 + γ 1 α 1 + α 3 γ V 2 1 + α 2 = V α + 1 3 γ + 1 2 γ 2 4 α γ + β η 1 6 α γ 2 + α β η 1 + 2 β γ η 1 + 2 α β γ η 1
This expression is positive for 2 γ 2 + β η 1 1 + 2 γ > α 4 γ + 6 γ 2 β η 1 1 + 2 γ , which is always true when 4 γ + 6 γ 2 β η 1 1 + 2 γ < 0 or equivalently when β η 1 > 2 γ 2 + 3 γ 1 + 2 γ . If β η 1 < 2 γ 2 + 3 γ 1 + 2 γ , then the expression is positive for α < 2 γ 2 + β η 1 1 + 2 γ 4 γ + 6 γ 2 β η 1 1 + 2 γ .
This expression is negative if 2 γ 2 + β η 1 1 + 2 γ < α 4 γ + 6 γ 2 β η 1 1 + 2 γ , which can only hold for 4 γ + 6 γ 2 β η 1 1 + 2 γ > 0 β η 1 < 2 γ 2 + 3 γ 1 + 2 γ , implying that α > 2 γ 2 + β η 1 1 + 2 γ 4 γ + 6 γ 2 β η 1 1 + 2 γ = 2 γ 2 + β η 1 1 + 2 γ 2 γ 2 + 3 γ β η 1 1 + 2 γ . This will always hold for β η 1 < 2 γ 1 + γ 1 + 2 γ since in this case, 2 γ 2 + β η 1 1 + 2 γ 2 γ 2 + 3 γ β η 1 1 + 2 γ < 1 .
The lemma concludes by combining the different cutoffs for A and B. □
An all-national equilibrium exists, leading to F B N N > F A N N when both conditions (A16) and (A17) are satisfied. For i A , this requires
β η 0 + η 1 α F A N N + F B N N 4 + γ σ N + Y 2 F B N N + V Π N > γ σ A + Y A Y B + α F A N N F B N N α F A N N + F B N N V
which becomes harder to satisfy when α increases since the LHS is decreasing in α and the RHS is increasing in α .29
For i B , the no-deviation condition for an all-national identification is given by
β η 0 + η 1 α F A N N + F B N N 4 + γ σ N + Y 2 F A N N + V Π N > γ σ B + Y B Y A α F A N N F B N N α F A N N + F B N N V
The RHS is now decreasing in α , but the first term on the LHS is decreasing, while the second is increasing,30 so there are opposing forces at play. To assess the overall effect, we introduce the corresponding mobilization efforts in an all-national equilibrium candidate into condition (A20) and collect all terms on the LHS and calculate the derivative with respect to α , which is given by
2 V γ 4 γ + β η 1 + 4 4 α + 2 γ + 6 α γ + 2 γ 2 + 2 α γ 2 + 2 α β η 1 + α β γ η 1 2 α + 2 γ + 2 α γ + α β η 1 + 2 3 > 0
So when α increases, the no-deviation condition for national identification by group B softens in an all-national candidate equilibrium.
We now check the condition when ethnic identification by A and national identification by B result in an equilibrium, leading to F A A N > F B A N . This requires condition (A16) to be violated and condition (A17) to be satisfied, which results in
γ σ A + Y A Y B + α F A A N F B A N α F A A N + F B A N V + 2 γ F B A N > β η 0 + η 1 α F A A N + F B A N 4 + γ σ N + Y + V Π N > γ σ B + Y B Y A α F A A N F B A N α F A A N + F B A N V + 2 γ F A A N
where the first line is due to group A, and the third line is due to group B. To check the incentives for group A to identify ethnically when B identifies nationally, we need to assess how the first inequality changes with α . For this purpose, we take everything to the LHS and assess the sign of the derivative with respect to α . Concentrating on the terms that change with α , we need to assess the derivative of
β η 1 α F A A N + F B A N 4 + γ 2 F B A N + α F A A N F B A N α F A A N + F B A N V
with respect to α , which, by tedious and straightforward calculations, can be shown to be positive.31 So group A is more likely to identify ethnically when group B identifies nationally when α increases.
For group B, national identification is indeed optimal when A identifies ethnically if
β η 0 + η 1 α F A A N + F B A N 4 + γ σ N + Y 2 F A A N + V Π N > γ σ B + Y B Y A α F A A N F B A N α F A A N + F B A N V
Taking everything to the LHS, we need to assess the sign of the derivative of
β η 1 α F A A N + F B A N 4 + γ α F A A N F B A N α F A A N + F B A N V 2 F A A N
with respect to α . Tedious calculations show that the sign depends on the sign of
352 α γ 2 32 γ 2 + 704 α γ 3 64 γ 3 + 608 α γ 4 32 γ 4 124 α β γ 2 η 1 12 β γ 2 η 1 + 200 α β γ 3 η 1 8 β γ 3 η 1 + 96 α β γ 4 η 1 + α β 2 γ η 1 2 + 12 α β 2 γ 2 η 1 2 + 12 α β 2 γ 3 η 1 2 + 16 α β γ η 1 8 β γ η 1 + 64 α γ + 192 α γ 5 α β 2 η 1 2 4 α β η 1 4 β η 1
Since α > 1 , the first four lines are positive. The entire expression increases with γ and is negative for small γ and positive for big γ . Hence, when status is sufficiently important, the no-deviation condition for B softens when α increases but tightens for sufficiently low γ .
For group A to identify nationally and B ethnically (resulting in F B N B > F A N B ) , condition (A16) needs to be satisfied, and condition (A17) needs to be violated, which leads to
γ σ A + Y A Y B + α F A N B F B N B α F A + F B N B V < β η 0 + η 1 α F A N B + F B N B 4 + γ σ N + Y 2 F B N B + V Π N < β η 0 + η 1 α F A N B + F B N B 4 + γ σ N + Y 2 F A N B + V Π N < γ σ B Y A Y B α F A N B F B N B α F A N B + F B N B V
The second and third lines are a direct consequence of F B N B > F A N B . Observe that in the first line, both α F A N B F B N B α F A + F B N B V and ( Y A Y B ) enter positively, while in the fourth line, they enter negatively, so unless group B is much richer than group A and/or its intrinsic status per se is much higher ( σ B > > σ A ), the condition cannot be satisfied simultaneously.

Appendix D. Proof of Proposition 6

We first derive the utility functions under the different identifications and the corresponding first-order conditions for f i when aid is non-exclusive but conditional on A controlling V.
Under ethnic identification of i A , the utility function of i is given by
y i f i + F A F V + Δ + γ σ A + Y A F A + F A F V + Δ Y B F B + F B F V + F A F Δ
which simplifies to
y i f i + F A F V + Δ + γ σ A + Y A Y B + F B F A + F A F B F V
leading to the first-order condition (FOC)
F B V + Δ + 2 γ V = F 2 1 + γ
Under ethnic identification of i B, the utility function of i is
y i f i + F B F V + F A F Δ + γ σ B + Y B F B + F B F V + F A F Δ Y A F A + F A F V + Δ
which simplifies to
y i f i + F B F V + F A F Δ + γ σ B + Y B Y A + F A F B + F B F A F V
leading to the FOC
F A V Δ + 2 γ V = F 2 1 + γ .
This requires V > Δ 1 + 2 γ for f i B > 0 .
Under national identification of i A , the utility function of i is
y i f i + F A F V + Δ β η 0 + η 1 F 4 + γ σ N + Y F + F A F V + Δ + F B F V + F A F Δ Π N
The FOC with respect to mobilization efforts is given by
1 + γ + β η 1 4 F 2 = F B V + Δ 1 + 2 γ
Under national identification of i B , the utility function of i is
y i f i + F B F V + F A F Δ β η 0 + η 1 F 4 + γ σ N + Y F + F A F V + Δ + F B F V + F A F Δ Π N
leading to the FOC
F 2 1 + β η 1 4 + γ = F A V Δ 1 + 2 γ .
This requires V > Δ 1 + 2 γ for f i B > 0 . Since Δ 1 + 2 γ > Δ 1 + 2 γ , we need to restrict V > Δ 1 + 2 γ to guarantee an interior equilibrium in mobilization efforts in all cases.
We now are in a position to derive the all-ethnic and all-national candidate equilibria. Combining (A22) and (A24) in an all-ethnic candidate equilibrium, group mobilization efforts are given by
F A A B = V 1 + 2 γ Δ V 1 + 2 γ + Δ 2 4 1 + γ 1 + 2 γ V 2
F B A B = V 1 + 2 γ Δ 2 V 1 + 2 γ + Δ 4 1 + γ 1 + 2 γ V 2
and
F A B = 1 + 2 γ V 1 + 2 γ Δ V 1 + 2 γ + Δ 2 V 1 + γ 1 + 2 γ 2
Combining (A26) and (A28), the group mobilization efforts in an all-national identification candidate equilibrium are given by
F A N N = V Δ 1 + 2 γ V + Δ 1 + 2 γ 2 1 + β η 1 4 + γ 4 V 2
F B N N = V Δ 1 + 2 γ 2 V + Δ 1 + 2 γ 1 + β η 1 4 + γ 4 V 2
F N N = V Δ 1 + 2 γ V + Δ 1 + 2 γ 1 + β η 1 4 + γ 2 V
Simple algebra reveals that
Corollary A5.
F N N < F A B .
Now we study the no-deviation condition (10). For given mobilization efforts, identifying ethnically is better than nationally for i A if and only if (A21) > (A25) or equivalently whenever
γ σ A + Y A Y B + F B F A + F A F B F V > β η 0 + η 1 F 4 + γ σ N + Y F + F A F V + Δ + F B F V + F A F Δ Π N
which simplifies to
β η 0 + η 1 F 4 > γ σ N σ A + 2 Y B 2 F B + V + 2 F A F Δ F A F B F V Π N
Observe that in the all-ethnic candidate equilibrium, F A B Δ < 0 since s i g n F A B Δ = s i g n 2 Δ and F B A B Δ < 0 since s i g n F B A B Δ = s i g n V 1 + 2 γ 3 Δ . Moreover,
2 F A A B F A B Δ F A A B F B A B F A B V = V 1 + 2 γ + Δ V 1 + 2 γ Δ Δ V V 1 + 2 γ = Δ + 2 V γ Δ V 1 + 2 γ
which is increasing in Δ . Therefore the LHS of condition (A30) decreases in Δ , while the RHS increases in Δ ; hence the condition tightens when Δ increases, so the set of parameters for which an all-ethnic equilibrium exists shrinks for group A .
Next we consider the no-deviation condition from ethnic identification for i B , which is derived from (A23 ) > ( A27) and simplifies to
β η 0 + η 1 F A B 4 > γ σ N σ B + 2 Y A 2 F A A B + V + 2 F A A B F A B Δ F B A B F A A B F A B V
The terms depending on the mobilization effort of the RHS in the all-ethnic candidate equilibrium can be rewritten as
V 1 + 2 γ Δ V 1 + 2 γ + Δ 2 2 1 + γ 1 + 2 γ V 2 + 2 V 1 + 2 γ + Δ 2 V 1 + 2 γ Δ + Δ V 1 + 2 γ V = 1 V 1 + 2 γ V 1 + 2 γ Δ V 1 + 2 γ + Δ 2 2 1 + γ 1 + 2 γ V + V 1 + 2 γ + Δ Δ + Δ
The sign of the derivative with respect to Δ is equal to the sign of
V 1 + 2 γ + Δ 2 + 2 V 1 + 2 γ Δ V 1 + 2 γ + Δ 2 1 + γ 1 + 2 γ V + V 1 + 2 γ + 2 Δ + V = 1 2 V 2 γ 2 + 3 γ + 1 8 V 2 γ 3 + 16 V 2 γ 2 + 12 V 2 γ + 3 V 2 + 8 V Δ γ 2 + 16 V Δ γ + 6 V Δ + 3 Δ 2 > 0
So the RHS is increasing in Δ , while the LHS is decreasing in Δ , resulting in the tightening of the no-deviation condition. Hence, ethnic identification becomes harder for group B in an all-ethnic equilibrium candidate.
Now we examine the no-deviation conditions for an all-national equilibrium candidate of i B . This requires condition ( ) < ( A27) so that
β η 0 + η 1 F N N 4 < γ σ N σ B + 2 Y A 2 F A N N + V + 2 F A N N F N N Δ + F A N N F B N N F N N V
The LHS is decreasing in Δ since F N N Δ < 0 . As for the RHS, both F A N N F N N Δ = V + Δ 1 + 2 γ 2 V Δ and F A N N F B N N F N N = Δ 1 + 2 γ V are increasing in Δ , but how F A N N changes with Δ depends on the size of Δ since s i g n F A N N Δ = s i g n V 3 Δ 1 + 2 γ . However, combining
2 F A N N + F A N N F B N N F N N = V Δ 1 + 2 γ V + Δ 1 + 2 γ 2 1 + β η 1 4 + γ 2 V 2 + Δ 1 + 2 γ
and calculating its derivative with respect to Δ , we get
1 V 2 2 γ + 1 4 γ + β η 1 + 4 24 Δ 2 γ 2 + 4 V 2 γ + 24 Δ 2 γ + 4 V Δ + 2 V 2 + 6 Δ 2 + 8 V Δ γ + V 2 β η 1 > 0 .
So the entire RHS is increasing in Δ , and the condition that an all-national candidate equilibrium is indeed an equilibrium for group B is relaxed.32

Appendix E. Proof of Proposition 7

We first derive utility functions under the different identifications and the corresponding first-order conditions for f i when aid is exclusively given to group A conditional on A controlling V .
Under ethnic identification of group A, the utility of individual i A is given by
y i f i + F A F V + Δ + γ σ A + Y A F A + F A F V + Δ Y B F B + F B F V = y i f i + F A F V + Δ + γ σ A + Y A Y B + F B F A + F A F Δ + F A F B F V
leading to the FOC
F 2 1 + γ = F B V 1 + 2 γ + Δ 1 + γ
Under ethnic identification of group B, the utility of individual i B is given by
y i f i + F B F V + γ σ B + Y B F B + F B F V Y A F A + F A F V + Δ = y i f i + F B F V + γ σ B + Y B Y A + F A F B + F B F A F V F A F Δ
leading to the FOC
F 2 1 + γ = F A V 1 + 2 γ + Δ γ .
If i A identifies nationally, the utility function is
y i f i + F A F V + Δ β η 0 + η 1 F 4 + γ σ N + Y F + F A F V + Δ + F B F V Π N
leading to the FOC
1 + γ + β η 1 4 F 2 = F B V + 1 + γ Δ
If i B identifies nationally, the utility function is
y i f i + F B F V β η 0 + η 1 F 4 + γ σ N + Y F + F A F V + Δ + F B F V Π N
leading to the FOC
1 + γ + β η 1 4 F 2 = F A V γ Δ
which requires V > γ Δ .
We are now in a position to derive the all-ethnic and all-national candidate equilibria. Combining (A34) and (A36), the mobilization efforts in an all-ethnic equilibrium candidate are given by
F B A B = V 1 + 2 γ + Δ 1 + γ V 1 + 2 γ + Δ γ 2 1 + γ 2 V + Δ 2 1 + 2 γ 2
F A A B = V 1 + 2 γ + Δ 1 + γ 2 V 1 + 2 γ + Δ γ 1 + γ 2 V + Δ 2 1 + 2 γ 2
and
F A B = V 1 + 2 γ + Δ 1 + γ V 1 + 2 γ + Δ γ 1 + γ 2 V + Δ 1 + 2 γ
Combining (A38) and (A40), we can calculate the fighting efforts in an all-national equilibrium candidate as follows:
F A N N = V γ Δ V + 1 + γ Δ 2 1 + γ + β η 1 4 2 V + Δ 2
F B N N = V γ Δ 2 V + 1 + γ Δ 1 + γ + β η 1 4 2 V + Δ 2
and
F N N = V γ Δ V + 1 + γ Δ 1 + γ + β η 1 4 2 V + Δ
Simple calculus reveals the following:
Corollary A6.
F N N < F A B .
We now determine the no-deviation condition (10) for an all-ethnic equilibrium. The no-deviation condition for an all-ethnic equilibrium for i A is given by (A33) > (A37), which reduces to
β η 0 + η 1 F A B 4 > γ σ N σ A + 2 Y B 2 F B A B + 2 F B A B F A B V Π N .
Observe that in an all-ethnic candidate equilibrium, F A B Δ > 0 since s i g n F A B Δ = s i g n 4 V 2 γ 2 + 4 V 2 γ + V 2 + 4 V Δ γ 2 + 4 V Δ γ + Δ 2 γ 2 + Δ 2 γ , so the LHS of (A42) is increasing in Δ . To sign the RHS, observe that
F B A B F A B Δ = 1 2 V + Δ 3 2 V + 2 V γ + Δ γ 2 γ 2 + 3 γ + 1 < 0
and
s i g n F B A B Δ = s i g n 8 V 3 γ 3 + 8 V 3 γ 2 + 2 V 3 γ + 12 V 2 Δ γ 3 + 12 V 2 Δ γ 2 + V 2 Δ γ V 2 Δ + 6 V Δ 2 γ 3 + 6 V Δ 2 γ 2 + Δ 3 γ 3 + Δ 3 γ 2 .
A sufficient condition for the term in brackets to always be positive is that γ > 1 7 . Hence, for γ > 1 7 , the RHS of (A42) is always decreasing in Δ , and the condition for an all-ethnic equilibrium is relaxed. If γ < 1 7 , then to sign the RHS of (A42), we evaluate the sign of the derivative of
F B A B + F B A B F A B V = V 1 + 2 γ + Δ 1 + γ V 1 + 2 γ + Δ γ 2 1 + γ 2 V + Δ 2 1 + 2 γ 2 + V 1 + 2 γ + Δ γ 1 + γ 2 V + Δ 2 1 + 2 γ
with respect to Δ . The sign is given by
8 V 3 γ 3 + 8 V 3 γ 2 + 2 V 3 γ + 12 V 2 Δ γ 3 + 12 V 2 Δ γ 2 + V 2 x γ V 2 Δ + 6 V Δ 2 γ 3 + 6 V Δ 2 γ 2 + 4 V γ 2 + 6 V γ + 2 V + Δ 3 γ 3 + Δ 3 γ 2 + 2 Δ γ 2 + Δ γ
The term in the bracket is increasing in γ and at γ = 0 is given by V 2 Δ + 2 V = V ( 2 V Δ ) , which is positive if Δ < V 2 , in which case the RHS of (A42) is decreasing in Δ , and hence the condition for ethnic identification in an all-ethnic equilibrium candidate relaxes for i A when Δ increases.
The no-deviation condition for an all-ethnic equilibrium for i B is given by (A35) > (A39), which reduces to
β η 0 + η 1 F A B 4 > γ σ N σ B + 2 Y A 2 F A A B + 2 F A A B F A B V + Δ Π N .
In an all-ethnic equilibrium candidate, the LHS is increasing in Δ . How the RHS changes with Δ depends on the sign of the derivative of F A A B + F A A B F A B V + Δ with respect to Δ , which is given by
1 γ + 1 2 V + x 3 2 γ + 1 2 * 8 V 3 + 12 V 2 x + 6 V x 2 + x 3 γ 3 + 16 V 3 4 V 2 + 24 V 2 x 2 V x + 12 V x 2 + 2 x 3 γ 2 + 10 V 3 6 V 2 + 13 V 2 x 5 V x + 6 V x 2 + x 3 γ + 2 V 2 x 2 V x + 2 V 3 2 V 2
Clearly, a sufficient condition for the term in the big bracket to be positive is V > 1 . With this assumption, the entire derivative is negative, and the condition for an all-ethnic identification softens for i B .
To summarize, a sufficient condition constituting that an increase in Δ makes an all-ethnic equilibrium more likely is V > max 2 Δ , 1 when γ < 1 7 or V > max γ Δ , 1 when γ 1 7 .

Appendix F. Proof of Proposition 8

We first derive the all-ethnic candidate equilibrium and check the effect of aid conditional on the ethnic identification of A .
Observe that in this case, where individuals identify ethnically, the utility function of i A coincides with the utility function under ethnic identification when only group A obtains conditional aid and is given by (A33). Similarly, for i B , the utility function under ethnic identification is given by (A35). Therefore, the all-ethnic candidate equilibrium is the same as the one derived in Appendix E. What differs is the no-deviation condition for i A . If in an all-ethnic candidate equilibrium, a member of group A deviated to national identification, this is a unilateral deviation (everybody else in the group still identifies as national), then the payoff from deviating to national identification for i A is given by
y i f i + F A F V β η 0 + η 1 F 4 + γ σ N + Y F + F A F Δ + V Π N
since everybody else in group A still identifies ethnically and enjoys Δ when i deviates to national identification. The no-deviation condition for member i of group A to prefer to identify ethnically in an all-ethnic equilibrium candidate requires (A33) > (A43), which simplifies to
β η 0 + η 1 F A B 4 + F A A B F N N Δ > γ σ N σ A + 2 Y B 2 F B A B + V Π N F A A B F B A B F A B V
We already know from the proof of Proposition 7 that F A B is increasing in Δ . Simple algebra shows that so is F A A B F N N Δ = V 1 + 2 γ + Δ 1 + γ 1 + γ 2 V + Δ 2 1 + 2 γ Δ ; hence the LHS is increasing in Δ . Concerning the RHS, F A A B F B A B F A B is increasing in Δ for 2 V > Δ , and F B A B is always increasing in Δ ; since both these expressions enter negatively, the RHS is decreasing in Δ for 2 V > Δ . Therefore, V > Δ 2 is a sufficient condition for the no-deviation condition to soften for i A , i.e., ethnic identification becomes more likely.
Since i B deviating to national identification will not affect whether aid is given to group A, the no-deviation condition for i B not to deviate to a national identification in an all-ethnic equilibrium candidate is exactly the same as that in the proof of Proposition 7 and so are the mobilization efforts; hence the very same proof holds in the present case. Hence, for V > max 1 , Δ 2 , an all-ethnic equilibrium becomes more likely when Δ increases for both groups.
We now derive the all-national candidate equilibrium and study the effect of aid conditional on ethnic identification on the respective no-deviation conditions. If group A identifies nationally, no aid is received, so the utility function for i A under national identification is identical to that under national identification in Sambanis and Shayo (2013), namely
y i f i + F A F V β η 0 + η 1 F 4 + γ σ N + Y F + F A F V + F B F V Π N
with the FOC
F B V = 1 + γ + β η 1 4 F 2
Similarly, for group B, the utility function is
y i f i + F B F V β η 0 + η 1 F 4 + γ σ N + Y F + F B F V + F A F V Π N
and mobilization efforts in an all-national candidate equilibrium are given by
F A N N = F B N N = V 4 1 + γ + β η 1 4
From (A47), it is clear that mobilization efforts with an all-national identification are independent of Δ . A member of group B cannot gain access to Δ by deviating to ethnic identification; hence the no-deviation condition of a member of group B for an all-national candidate equilibrium is unaffected by Δ . The no-deviation condition of a member of group A depends on whether or not an individual deviation to ethnic identification gives them access to aid when group A controls V. If yes, the incentives to deviate become stronger. If a one-sided deviation does not provide access to aid, the no-deviation condition of i A is unaffected by an increase in Δ .
Simple algebra reveals the following:
Corollary A7.
F N N = 2 F A N N < F A B where F A B is given by Equation (A41), and F A B Δ > 0 .

Appendix G. Proof of Proposition 10

If a foreign actor gives aid Δ conditional on national identification and group A controlling V in the case of national identification by both groups, the utility functions coincide with the case of conditional aid which is enjoyed by both groups and are therefore given by (A25) for group A and (A27) for group B, and the corresponding group mobilization efforts for an all-national equilibrium candidate are derived in the proof of Proposition 6, and we need to assume that V Δ 1 + 2 γ for the interior mobilization efforts of both groups.
The no-deviation condition for i A is
y i f i + F A N N F N N V + Δ β η 0 + η 1 F N N 4 + γ σ N + Y F N N + F A N N F N N V + Δ + F B N N F N N V + F A N N F N N Δ Π N > y i f i + F A N N F N N V + γ σ A + Y A F A N N + F A N N F N N V + Δ Y B F B N N + F B N N F N N V + F A N N F N N Δ
Everybody except the deviating i still receives aid because they stick to national identification. The condition simplifies to
F A N N F N N Δ + γ σ N σ A + 2 Y B 2 F B N N + 2 F B N N F N N V + 2 F A N N F N N Δ Π N > β η 0 + η 1 F N N 4
Since V > Δ 1 + 2 γ , the expression F B N N is decreasing in Δ . Using the derivation in the proof of Proposition 6, the only term that does not relax the above condition is F B N N F N N V . Observe that the derivative of
2 F B N N F N N V + 2 F A N N F N N Δ = V Δ 1 + 2 γ + V + Δ 1 + 2 γ Δ
is V + 2 Δ 2 γ + 4 Δ γ 1 , which is always positive if V > 1 + 2 γ , so V > 1 + 2 γ is a sufficient condition for the no-deviation condition for a member of A to be relaxed.
The no-deviation condition for i B to not deviate from an all-national equilibrium candidate is
y i f i + F B N N F N N V + F A N N F N N Δ β η 0 + η 1 F N N 4 + γ σ N + Y F N N + F A N N F N N V + Δ + F B N N F N N V + F A N N F N N Δ Π N > y i f i + F B N N F N N V + γ σ B + Y B F B N N + F B N N F N N V + F A N N F N N Δ Y A F A N N + F A N N F N N V + F A N N F N N Δ
given that everybody who does not deviate still receives aid. This simplifies to
F A N N F N N Δ + γ σ N σ B + 2 Y A 2 F A N N + 2 F A N N F N N V + Δ Π N > β η 0 + η 1 F N N 4
From the proof of Proposition 6, we know that the sign of F A N N Δ is ambiguous, but we already showed in the proof that if we combine 2 F A + 2 F A F Δ and calculate the derivative with respect to Δ , the sign is positive, so (A48) in an all-national equilibrium candidate is relaxed when Δ increases.
Concerning the case where everybody identifies ethnically, the utility functions are identical to the ethnic identification in Sambanis and Shayo (2013) given by
y i f i + F A F V + γ σ A + Y A F A + F A F V Y B F B + F B F V
for group A and
y i f i + F B F V + γ σ B + Y B F B + F B F V Y A F A + F A F V
resulting in the following mobilization efforts in an all-ethnic equilibrium candidate
F A A B = F B A B = ( 1 + 2 γ ) ( 1 + γ ) V 4
Hence, mobilization efforts are not affected by Δ in this candidate equilibrium. Because both identifying ethnically as a member of group B when group A identifies ethnically and identifying nationally as a member of group B when group A identifies ethnically are independent of aid for group B, the condition for a member of group B to choose ethnic over national identification is unaffected by changes in Δ . The same applies to a member of group A if aid requires national identification by the entire group rather than just the individual. However, if an individual from group A can receive aid even when they are the only one identifying nationally, this tightens the no-deviation condition for that person.
Simple calculus reveals the following:
Corollary A8.
F A B > F N N where F N N is given by Equation (A29).
[custom]

Notes

1
This utility function extends Akerlof and Kranton (2000), who were the first to model identity as an ingredient in the utility function.
2
Several studies have applied this utility function to study individuals’ self-identification in different institutional contexts. Shayo (2009) himself and Lindqvist and Östling (2013) apply this utility function to analyze the demand for redistribution. Penn (2008) and Penn (2009) examine electoral institutions, Holm (2016) applies the approach to federations, and Grossman and Helpman (2021) analyze a Heckscher–Ohlin trade setting. They explain why broad national identification induces inequality aversion and protectionist tariffs and how populist shifts to narrow class identity can trigger discrete jumps in trade policy. Farmer (2025) synthesizes these insights to account for the resurgence of protectionism and social conservatism in the United States. Finally, Atkin et al. (2021) provide an empirical application in consumption, showing that identity salience responds to economic costs in food choices.
3
We also refer to a national social identity as a civic social identity.
4
An early example where altruism is modeled linearly is Hausken (1996).
5
The pioneering work of Akerlof and Kranton (2000) on identity introduces identity as a linear component in the utility function.
6
When we study conditional aid, the intervener will alter the prize of the contest, and this new prize might be group-dependent.
7
The choice of contest success function (CSF) is central to modeling resource conflicts between two groups. Among the various specifications—such as ratio-based, difference-based, and generalized Tullock forms—the ratio CSF, which we use in the present paper, has become the canonical baseline. This form is justified on several grounds. Axiomatic derivations show that under symmetry and independence of irrelevant alternatives, the ratio CSF is essentially unique (Clark & Riis, 1998; Skaperdas, 1996). It also admits a stochastic interpretation: when each unit of effort is subject to independent exponential noise, success probabilities become proportional to resource shares (Jia, 2008). Furthermore, the ratio form offers analytical tractability, enabling smooth comparative statics and equilibrium characterization. Empirical evidence reinforces its plausibility: studies of historical and virtual battles (Hwang, 2009; Massoni et al., 2016) find that relative effort models outperform difference-based alternatives. Intuitively, the ratio CSF reflects a lottery analogy, where each unit of resource acts as a ticket, ensuring scale invariance and fairness. Moreover, the ratio form is used by Sambanis and Shayo (2013), whose work serves as our baseline model. For these reasons, we adopt the ratio form as a theoretically sound, empirically validated, and strategically robust specification.
8
Observe that individuals cannot alter their ethnicity; they only choose their self-identification as ethnic or national.
9
This is the standard Nash equilibrium condition.
10
We will clarify the exact assumption for f i > 0 when we analyze the different intervention forms. The required assumption for f i < y i is that equilibrium F J < Y J .
11
For the first intervention we study, we will provide all mathematical derivations in the main text and relegate the details of other interventions to the Appendices.
12
Second-order conditions are 2 F F A F + E A 3 V < 0 for i A and 2 F + F F A F B F + E A 3 V < 0 for i B .
13
The subscript of F refers to the subgroup under consideration, while the first superscript refers to the chosen identity of group A and the second to the chosen identity of group B. Group A can either identify ethnically, denoted by A, or nationally, denoted by N . Similarly, group B can either identify ethnically, denoted by B, or nationally, denoted by N .
14
The possibility of multiplicity is established in Proposition 1 in Sambanis and Shayo (2013). Multiplicity can occur in all types of foreign interventions we study in the present paper. Recall that when the size of the studied foreign interventions approaches zero, our model reduces to Sambanis and Shayo (2013)’s model.
15
We do not model the resources provided by the intervener that lead to this technological enhancement. Individuals in the target country know the efficiency of the mobilization technologies of the different groups; in other words, they know the constants α J and α J before making their decisions.
16
By Corollary A1 in Appendix B, mobilization resources are the highest under all-ethnic identification.
17
In Appendix C, we derive the conditions for an equilibrium in which group A identifies nationally and B ethnically. We show that these conditions are not likely to be simultaneously satisfied under one-sided technological improvements in conflict technology. Therefore, we do not study this candidate equilibrium any further.
18
The exact conditions for how an increase in α affects the likelihood of an all-ethnic equilibrium are given in Appendix C in Lemma A4.
19
The difference in success probabilities in favor of the group helped by the foreign intervener is the lowest if both groups identify nationally, but interestingly, it is higher if one group identifies ethnically and one nationally than if both identify ethnically no matter which group identifies ethnically. Simple calculus by pairwise comparison reveals that α F A A B F B A B α F A A B + F B A B > α F A N N F B N N α F A N N + F B N N and α F A A B F B A B α F A A B + F B A B < α F A N B F B N B α F A N B + F B N B and α F A A B F B A B α F A A B + F B A B < α F A A N F B A N α F A A N + F B A N , but the comparison between α F A N B F B N B α F A N B + F B N B and α F A A B F B A B α F A A B + F B A B depends on underlying parameters.
20
For the case of one-sided technological enhancement, see Corollary A3 and Corollary A4 in Appendix C.
21
The exact upper bound on Δ depends on the type of conditional aid studied and will be stated in the corresponding Appendices where we derive the results.
22
Observe that in the present context, people self-identify as ethnic or national; hence the verification of ethnic or national identity is not an issue here.
23
It is important to realize that the no-deviation condition looks at a unilateral deviation. In the present context, the deviation implies that i deviates to a different identification, but everybody else maintains the prescribed identification with the relevant consequence on aid reception that is conditional on identification.
24
The derivative with respect to Δ is given by 4 V Δ + Δ 2 + 2 V 2 γ + Δ 2 γ + V 2 + 4 V Δ γ 2 V + Δ 2 2 γ 2 + 3 γ + 1 > 0 .
25
This follows from Proposition 2 in Sambanis and Shayo (2013).
26
This follows directly from Proposition 3 in Sambanis and Shayo (2013).
27
In particular,
F A N B α = 1 + 2 γ 2 1 + γ β η 1 2 1 + 2 γ 1 + γ + β η 1 α 4 + 1 + γ 3 V < 0
F B N B F A N B F N B α = 1 + 2 γ 1 + γ β η 1 2 1 + 2 γ 1 + γ + β η 1 α 4 + 1 + γ 2 > 0
α F N B α = 2 γ + 1 2 2 γ + 1 1 + 2 γ 1 + γ + β η 1 α 4 + 1 + γ 2 V > 0
28
Observe that
F B N B α = 1 + 2 γ 2 β η 1 4 1 + 2 γ 1 + γ + β η 1 α 4 + 1 + γ β η 1 2 1 + 2 γ 3 1 + γ + β η 1 α 4 1 + 2 γ 1 + γ + β η 1 α 4 + 1 + γ 3 V < 0
29
Observe that
F B N N α = V 1 8 α 2 β 2 η 1 2 + 1 4 α 2 β γ η 1 + 1 4 α 2 β η 1 + 1 2 α β γ η 1 + 1 2 α β η 1 + γ 2 + 2 γ + 1 β η 1 α 2 + 1 + γ 1 + α 3 > 0
α F A N N + F B N N α = V 1 + γ 1 + α β η 1 α 2 + 1 + γ 1 + α 2 > 0
α F A N N F B N N α F A N N + F B N N α = γ + 1 2 γ + 1 2 β η 1 + 2 1 + γ α + 1 + α β η 1 2 2 > 0
30
F A N N α = 1 + β η 1 4 + γ 1 + γ α β η 1 2 + 1 + γ β η 1 α 2 + 1 + γ 1 + α 3 < 0
31
The derivative is 4 V 2 γ 2 + 3 γ + 1 4 α + 4 γ + 12 α γ + 8 α γ 2 + α β η 1 + 2 α β γ η 1 + 4 3 *
64 γ + 96 γ 2 + 32 γ 3 + 4 β η 1 + 32 α γ 2 + 96 α γ 3 + 64 α γ 4 + 8 β γ 2 η 1 + α β 2 η 1 2 + 4 α β η 1 + 12 β γ η 1 + 40 α β γ 2 η 1 + 32 α β γ 3 η 1 + 4 α β 2 γ η 1 2 + 20 α β γ η 1 + 4 α β 2 γ 2 η 1 2
32
What happens to the corresponding condition for group A cannot be established, in general, since the corresponding expression on the RHS cannot be ranked due to F A N N F B N N F N N diminishing the expression, and even combined derivatives do not yield a clear-cut solution.

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