Cooperation Collapse in the Harmony Game: Revisiting Scodel and Minas Through Evolutionary Game Theory

Abstract

Between 1959 and 1962, Alvin Scodel, J. Sayer Minas, and colleagues conducted some of the earliest laboratory studies of strategic interaction using non-zero-sum games. Working at the margins of economics in the Journal of Conflict Resolution, they documented a striking pattern: subjects frequently chose options that reduced an opponent’s payoff by more than their own, even when mutual cooperation was both individually and collectively optimal. These results—especially the behavior observed in their so-called Game H4, a Harmony Game in which cooperation strictly dominated defection—anticipate a central insight of evolutionary game theory: what matters for adaptation is relative payoff, not absolute gain. This essay reinterprets the Scodel–Minas experiments through a Darwinian lens, arguing that they provide an early empirical challenge to Nash-equilibrium reasoning and to models that evaluate strategies solely in terms of absolute utility. By reconstructing the H4 payoff structure and embedding it within a simple evolutionary framework, I show how small levels of “competitive” behavior can destabilize cooperative equilibria that appear self-evident under standard assumptions. I then revisit three later “puzzles” in the evolution of cooperation—altruistic punishment, the fragility of “win–win” treaties, and rejections in ultimatum bargaining—to ask how differently they might have been framed had the Scodel–Minas findings been part of the canonical experimental literature. Rather than treating these phenomena as surprising anomalies, a historically informed, relative-payoff perspective suggests that they could have been recognized much earlier as natural expressions of an already documented pattern.

1. Introduction

Cooperation in social dilemmas is often treated as a triumph of rational design over short-run self-interest. Work on repeated interaction, reputation, and institutional enforcement has shown how cooperation can be sustained even when unilateral defection is tempting (Axelrod, 1984; Axelrod & Hamilton, 1981; Gintis, 2000; Hofbauer & Sigmund, 1998; Nowak, 2006; Ostrom et al., 1992). More broadly, a large literature now explores how prosocial behavior can evolve under natural selection and cultural learning, shaping outcomes from microbes to human societies (Nowak, 2006; Perc & Szolnoki, 2010).

At the same time, for decades the Nash equilibrium has provided the organizing concept for strategic reasoning in economics and game theory (Nash, 1950). A Nash equilibrium is a profile of strategies in which no player can improve her payoff by deviating unilaterally. When a game is constructed so that cooperation is both individually and collectively optimal, standard reasoning suggests that cooperation should be observed, at least under conditions approaching common knowledge of rationality.

This essay revisits a series of largely forgotten experiments by Scodel, Minas, and co-authors in the late 1950s and early 1960s. These studies—conducted in psychology and political science departments and published in the Journal of Conflict Resolution—preceded the rise of both experimental economics and evolutionary game theory (Minas et al., 1960; Scodel, 1962; Scodel et al., 1959). Yet their results foreshadow a key insight of the evolutionary approach: human subjects often behave as if relative payoffs, not absolute gains, are what matter.

In particular, I focus on a treatment that Scodel and Minas called Game H4. By modern terminology, H4 is a Harmony Game: for each player, cooperation strictly dominates defection, and mutual cooperation yields the highest joint payoff. From the perspective of static game theory, the cooperative Nash equilibrium should be compelling. Instead, Scodel and Minas found that in roughly three quarters of plays at least one subject defected, undermining the cooperative outcome (Minas et al., 1960).

The goals of this essay are threefold. First, I reconstruct the Scodel–Minas experiments with particular attention to H4, situating their work historically in relation to Nash equilibrium and early experimental game theory. Second, I provide a simple evolutionary reinterpretation, embedding the H4 payoff structure in an informal replicator dynamic and treating “competitive” choices as attempts to improve relative position. Third, I turn to three later literatures—on altruistic punishment, “win–win” treaties, and ultimatum bargaining—and, rather than offering new explanations of their now-familiar findings, ask how differently those phenomena might have been understood at the time had Scodel and Minas been part of the canonical experimental record.

2. Forgotten Experiments in Non-Zero-Sum Games

2.1. Scodel and Minas in Historical Context

Between 1959 and 1962, Alvin Scodel, J. Sayer Minas and colleagues reported a sequence of laboratory studies on two-person non-zero-sum games (Minas et al., 1960; Scodel, 1962; Scodel et al., 1959). At the time, game theory remained largely a mathematical enterprise, and the idea of bringing normal-form payoff matrices into the laboratory was still novel. Their work therefore predates the canon of experimental economics as well as the evolutionary turn in game theory. In the folk history of experimental economics, however, the field is often said to begin in the early 1960s with Vernon Smith’s double-auction market experiments, especially his 1962 article “An Experimental Study of Competitive Market Behavior,” (Smith, 1962) which is widely regarded as a foundational contribution to the methodology of the field (Roth, 1993, 1995). From that vantage point, the Scodel–Minas games appear only as peripheral precursors, even though they already employed incentivized laboratory play in formally specified non-zero-sum games several years before Smith’s market study appeared in print.

Because these experiments appeared in a political science and psychology journal rather than a mainstream economics outlet, they were largely overlooked in the subsequent development of game theory. They were not completely invisible, however. Roth’s early historical survey of experimental economics and his introduction to Kagel and Roth’s Handbook of Experimental Economics list the Scodel–Minas papers among the early laboratory studies of interactive decision making, but only as one item in a broad catalog rather than as a central case study (Roth, 1993, 1995). Yet they contain remarkably prescient observations about human responsiveness to relative payoffs. Scodel and Minas repeatedly interpret behavior as “competitive” or “aggressive”, even when this reduces the absolute payoffs of all (Minas et al., 1960).

Even within the experimental literature, their impact has remained modest: citation counts for Minas et al. (1960), vary sharply by index, ranging from 37 in Scopus to 182 in Google Scholar (both accessed 30 January 2026); these discrepancies likely reflect differences in coverage and duplicate/split records for similarly titled companion papers (I–III). Even taking the upper bound, this is small (less than three citations/year) relative to the citation footprint of canonical Prisoner’s Dilemma experiments and early cooperation research from the same era that became standard reference points.

2.2. The Structure of the Scodel–Minas Games

Across several studies, Scodel and co-authors presented pairs of subjects with $2\times 2$ payoff matrices of the familiar form

$$\begin{array}{ccc}& C& D\\ C& (R,R)& (S,T)\\ D& (T,S)& (P,P)\end{array}$$

(1)

in which each player chooses between a cooperative action C and a competitive or defecting action D. By varying the ordinal relations among T, R, P, and S, they implemented many distinct strategic environments, including versions of the Prisoner’s Dilemma and other zero-sum contests. In some treatments, payoffs were symmetric; in others, one player enjoyed a structural advantage.

Although their primary aim was descriptive—to catalog patterns of behavior across different payoff structures—some of their treatments implicitly tested the relative importance of absolute versus relative gains. Subjects were paid according to the matrix outcomes, typically in tokens convertible to money.

In most of these games, the observed behavior was mixed: subjects sometimes cooperated and sometimes defected, often in ways that departed from Nash predictions in familiar ways. What stands out, however, is a robust tendency for players to choose actions that reduced the opponent’s payoff by more than their own, particularly in situations where structural asymmetries made disparity salient. It was this tendency that led Minas and co-authors to conclude that performance was driven “in good part by a maximization-of-difference” (Minas et al., 1960, p. 197).

2.3. Game H4: When Cooperation Should Be Irresistible

The most striking evidence emerged from Game H4, defined by Scodel and colleagues as follows (Minas et al., 1960, p. 196):

$$\begin{array}{ccc}& C& D\\ C& (4,4)& (1,3)\\ D& (3,1)& (0,0)\end{array}$$

(2)

where, as before, C denotes a cooperative move and D a defecting or competitive move.

Several features of this payoff structure are important.

• For each player, C strictly dominates D: regardless of the opponent’s choice, $4>3$ and $1>0$.
• Mutual cooperation $(C,C)$ yields the highest joint payoff and the highest individual payoff for both players.
• The profile $(C,C)$ is, therefore, not only Pareto-efficient but also the unique Nash equilibrium in pure strategies.

From the standpoint of standard game theory, H4 should pose no dilemma at all. A player who reasons in terms of absolute payoffs and best responses will select C regardless of beliefs about the opponent. Given sufficient common knowledge of rationality, $(C,C)$ should be the natural prediction.

Scodel and colleagues found something very different. In 72% of H4 plays, at least one player chose D, and mutual defection $(D,D)$ occurred substantially more often than the Nash prediction of zero (Minas et al., 1960). Subjects willingly sacrificed payoff units to prevent the opponent from gaining more, thereby destabilizing an outcome that was secure in both Nash and Pareto terms.

Put differently, behavior in H4 revealed that subjects were not simply maximizing absolute payoffs. Instead, they appeared to be trading off absolute gains against relative position: for some participants, it was preferable to earn three when the opponent earned one than to earn four when the opponent also earned four. This pattern is precisely what one would expect if utility includes a concern for relative standing.

It is important to note that departures from dominance-solvable play can also arise from imperfect comprehension or low attention. Early laboratory protocols did not routinely include the comprehension checks, training rounds, and attention safeguards that are now standard in experimental economics, and modern labs still confront the possibility that some participants are distracted or misunderstand payoff descriptions (Roth, 1995). More broadly, experimental economists have long debated whether cooperative behavior in social dilemmas reflects stable prosocial motivations or, in part, confusion about incentives—famously framed as “kindness or confusion” (Andreoni, 1995). While such factors could contribute to some non-cooperative choices even in H4, Scodel and Minas’ own interpretation emphasizes a systematic pattern: subjects sometimes appeared to trade off absolute gains against payoff differences. This historical analysis, therefore, treats H4 defection not as a mere error term, but as evidence that interpersonal comparison can enter effective payoffs in a way that standard absolute-utility reasoning obscures.

3. From Nash to Darwin: A Simple Evolutionary Reinterpretation

3.1. Absolute vs. Relative Payoffs

The Nash equilibrium is defined purely in terms of absolute payoffs: each player chooses a best response given the strategies of others, and payoffs are evaluated independently for each player (Nash, 1950). If behavior is guided entirely by such absolute utilities, then H4 should reliably produce cooperation. Even modest levels of noise or bounded rationality are unlikely to overturn the strict dominance of C when the payoffs are as stark as in (2).

Evolutionary approaches, in contrast, model adaptation in terms of relative payoffs. In the simplest replicator dynamic, the growth rate of a strategy is proportional to the difference between its payoff and the population average (Hofbauer & Sigmund, 1998; Maynard Smith, 1982; Taylor & Jonker, 1978; Weibull, 1995). A strategy that earns slightly more than competitors will increase in frequency, even if all payoffs are low in absolute terms; conversely, a strategy can be driven to extinction despite high absolute payoffs if it consistently underperforms relative to rivals.

Human behavior is seemingly shaped by a hybrid of these two logics. Experimental and empirical work on status competition (Frank, 1985), inequity aversion (Fehr & Schmidt, 1999), and reference-dependent preferences (Bolton & Ockenfels, 2000; Solnick & Hemenway, 1998) all point toward utility functions that incorporate relative standing. What Scodel and Minas observed in H4 can be read as an early, if informal, recognition of this mixed payoff structure. In later economic terminology, such trade-offs are captured by models of interdependent preferences, in which an individual’s utility depends explicitly on the outcomes or consumption of others. A formal demand-theoretic treatment of interdependent preferences was developed in the 1970s by Duesenberry, Becker, Pollak, and others, building on much earlier observations about social status and relative consumption (Becker, 1974; Duesenberry, 1949; Pollak, 1976; Postlewaite, 1998). From the perspective taken here, however, the empirical pattern that these models seek to represent was already visible in the Scodel–Minas data: subjects chose actions that sacrificed absolute income in order to alter payoff differences. In this sense, the modern literature on interdependent preferences owes—or should be seen as owing—an experimental lineage to their non-zero-sum games, even if that lineage has rarely been acknowledged explicitly.

3.2. A Toy Dynamic for H4

To illustrate how concerns for relative payoffs can undermine the cooperative Nash equilibrium in H4, consider a stylized evolutionary dynamic. Let x denote the fraction of the population playing C and $1-x$ the fraction playing D. Suppose that material payoffs are given by (2), but that the effective payoff (or fitness) of each strategy includes a penalty for being behind the opponent.

One simple way to capture this is to define, for player i,

$${\pi }_i=u_i-\alpha max\{0,u_j-u_i\},$$

(3)

where $u_i$ is the material payoff, $u_j$ the opponent’s payoff, and $\alpha \ge 0$ measures the strength of concern for disadvantageous inequality. When $\alpha =0$, players care only about absolute income; as $\alpha$ increases, they increasingly dislike being left behind.

In H4, the absolute payoffs for a focal C player are

$$\begin{array}{cc}\hfill u_C\left(x\right)& =4x+1(1-x)=1+3x,\hfill \end{array}$$

(4)

$$\begin{array}{cc}\hfill u_D\left(x\right)& =3x+0(1-x)=3x,\hfill \end{array}$$

(5)

so $u_C\left(x\right)>u_D\left(x\right)$ for all $x>0$. However, the relative penalty term differs across outcomes. When a cooperator meets a defector, she earns $(1,3)$ and suffers a disadvantage of two; when a defector meets a cooperator, he earns $(3,1)$ and suffers no disadvantage. Thus, for moderate $\alpha$, the effective payoffs can be ordered so that D is no longer dominated.

Under a replicator-type dynamic driven by $\pi$ instead of u, universal cooperation ($x=1$) remains a fixed point, but it need not be globally attracting. In the expected-payoff version of this toy model, the selection gradient can be written so that its sign depends on a simple term $1-2\alpha (1-x)$. This makes the role of $\alpha$ transparent: when $\alpha <1/2$, cooperation is globally attracting from any interior initial condition; when $\alpha >1/2$, the dynamic becomes bistable, with an unstable interior threshold $x^{*}=1-1/\left(2\alpha \right)$ separating basins of attraction for $x=0$ and $x=1$. In this sense the cooperative Nash equilibrium is fragile: sufficiently strong concern for disadvantageous comparisons, or a large enough initial minority of “competitive” play, can push the system below the threshold and trigger collapse toward widespread defection.

The linear disadvantageous-inequality term in (3) is chosen for transparency, not as a claim about the unique shape of social preferences. Allowing nonlinear comparison costs, reference-point effects, or preference components that also value advantageous inequality would generally shift the location of $x^{*}$ and the speed of convergence without changing the qualitative point: once effective payoffs incorporate interpersonal comparisons, dominance in absolute payoffs no longer guarantees global stability (Bolton & Ockenfels, 2000; Fehr & Schmidt, 1999).

Finally, the toy account treats $\alpha$ (or a “competitive” orientation) as fixed. In practice, learning and feedback can make social comparison more or less salient: displaying the opponent’s outcome prominently, emphasizing rank, or framing outcomes as contests may increase the weight placed on relative position, while designs that limit social comparison information may attenuate it (Roth, 1995). Endogenizing the emergence of competitive play through such mechanisms is, therefore, a natural extension of this framework and a bridge between experimental design and the likelihood of H4-style collapse.

3.3. Evolutionary Game Theory and Relative Fitness

The emphasis on relative outcomes is familiar in evolutionary game theory. In many models, fitness is defined only up to affine transformations: what matters is not the absolute level of payoffs but how they compare to others’, because selection amplifies strategies that do better than the population average (Hofbauer & Sigmund, 1998; Maynard Smith, 1982; Nowak, 2006; Weibull, 1995).

A terminological note is important. In standard infinite-population evolutionary game theory, “relative fitness” typically refers to payoff relative to the population average. Under that definition, H4 poses no evolutionary puzzle: because C strictly dominates D, cooperation maximizes both absolute payoff and relative fitness in the population-average sense, and standard replicator dynamics predict convergence to $x=1$.

The behavior Scodel and Minas emphasize—choosing $(3,1)$ over $(4,4)$ to secure a payoff advantage—instead reflects an interpersonal comparison motive: agents behave as if utility includes a preference for being ahead (or avoiding being behind) a particular opponent. This is closely related to the evolutionary theory of spite and payoff-difference maximization, including results showing that in finite populations selection can favor strategies that increase payoff gaps even at an absolute cost (Gardner & West, 2004; Possajennikov, 2000; Schaffer, 1988).

Notably, this theoretical literature developed largely independently of the Scodel–Minas experimental lineage, reinforcing the essay’s broader point about disciplinary silos: the mathematics of spite advanced even as early laboratory evidence of payoff-difference motives remained under-integrated in the canonical experimental record. The Scodel–Minas experiments can be seen as a human-subjects counterpart of this logic. Subjects appear to treat their partners as reference points and to care about maintaining or improving their relative standing, even at some cost to absolute gains.

This reinterpretation connects a neglected experimental tradition to the now vast literature on the evolution of cooperation. Instead of viewing the harmony-game results as an anomaly or as evidence of irrationality, we can understand them as revealing that human preferences incorporate a relative-payoff component. In the next section, I revisit three later “puzzles” in the cooperation literature and ask how differently they might have been framed had the Scodel–Minas findings been integrated into mainstream game theory at the time.

4. Later Cooperation Puzzles in Light of Scodel–Minas

By the early 1980s and 1990s, several empirical literatures had emerged in which human behavior in social dilemmas was described as puzzling relative to the predictions of standard game theory and narrow self-interest. Experimental economists and behavioral researchers wrote of altruistic punishment, surprisingly robust cooperation, and rejections of profitable offers as anomalies that demanded new theoretical tools (Fehr & Gächter, 2002; Güth et al., 1982; Henrich et al., 2001; Thaler, 1988). International-relations scholars debated why ostensibly “win–win” agreements so often failed, framing this as a challenge to liberal theories of absolute gains (Grieco, 1988; Shutters, 2016; Snidal, 1991).

The aim of this section is not to offer yet another explanation of these now-familiar phenomena. Instead, I adopt a historical perspective and ask a counterfactual question: had the findings of Scodel and Minas been part of the canonical game-theoretic and experimental literature, would these behaviors have been described as mysteries at all? Put differently, how might the narratives around these puzzles have differed if later authors had seen them as instances of a pattern already visible in the non-zero-sum experiments of 1959–1962?

4.1. Altruistic Punishment as an Unsurprising Pattern

When Fehr and Gächter (2002) introduced the term “altruistic punishment,” they emphasized that subjects were willing to incur costs to punish free riders in public-goods experiments, even though punishers received no direct material gain. This was presented, quite reasonably, as a challenge to the standard picture of self-interested agents and a key element in explaining the evolution of cooperation. Subsequent work extended these findings across societies and experimental designs, and a large literature grew up around fairness, reciprocity, and strong reciprocity (Bolton & Ockenfels, 2000; Espín et al., 2022; Fehr & Schmidt, 1999; Gintis, 2000; Henrich et al., 2001).

Had the Scodel–Minas results been widely known and integrated into economic thinking, the framing might have been less one of surprise and more one of continuity. In their non-zero-sum games, subjects already displayed a willingness to choose outcomes that reduced an opponent’s payoff by more than their own (Minas et al., 1960; Scodel, 1962; Scodel et al., 1959). In Game H4 in particular, players sometimes gave up a unit of absolute income (moving from 4 to 3) in order to create a two-unit advantage over their partner (3 vs. 1). Conceptually, this behavior is extremely close to what would later be labeled altruistic punishment: a costly action that lowers another’s payoff even more, thereby improving one’s relative standing.

Two clarifications sharpen the continuity with the Scodel–Minas pattern. First, whether costly punishment is perceived as “surprising” depends in part on institutional details: in public-goods environments, the prevalence and consequences of punishment vary with the punishment cost to the punisher (Boyd et al., 2003) and the fine imposed on the target, and evolutionary models show that punishment spreads only in particular regions of this cost–fine space (Helbing et al., 2010). Second, when individuals can choose among institutional environments, they often migrate toward sanctioning regimes that allow free-rider punishment, giving such institutions a competitive advantage over non-sanctioning alternatives (Gürerk et al., 2006).

From this counterfactual vantage point, the “mystery” of altruistic punishment in the early 2000s looks less like a fundamental anomaly and more like a rediscovery of a pattern documented four decades earlier in a different disciplinary silo. If experimental economists in the 1980s and 1990s had routinely cited Scodel and Minas alongside classical Prisoner’s Dilemma experiments, they might have treated costly punishment not as an unexpected departure from Homo economicus, but as further evidence that people trade off absolute gains against relative position in structured ways. The theoretical move toward inequity aversion and status-sensitive utility (Bolton & Ockenfels, 2000; Fehr & Schmidt, 1999; Frank, 1985) might still have been necessary, but the narrative of novelty would have been softened.

4.2. “Win–Win” Treaties and the Realist Critique

A similar point applies to the international-relations debates of the late 1980s and early 1990s. Liberal institutionalists argued that international institutions can facilitate mutually beneficial cooperation, casting many issues in Prisoner’s Dilemma or assurance-game terms. Realist critics pointed out that states care about relative as well as absolute gains, and that cooperation may fail when some parties benefit disproportionately (Grieco, 1988; Snidal, 1991). The resulting “relative gains” debate revolved around why treaties that appeared efficient on paper—trade agreements, arms control, environmental accords—so often stalled or unraveled.

In that literature, the failure of “win–win” treaties is frequently presented as a puzzle for purely absolute-gains models. Yet the behavior that troubled liberal theorists had already been observed experimentally by Scodel and Minas. In Game H4, a cooperative outcome that improved both players’ absolute payoffs was nevertheless unstable because some subjects preferred to avoid outcomes in which the other did equally well or better (Minas et al., 1960). Their language of “maximization-of-difference” anticipates the realist emphasis on relative gains almost verbatim.

A concrete illustration is the 1994 U.S.–North Korea Agreed Framework, which was designed as a quintessential “win–win” bargain: North Korea would freeze (and ultimately dismantle) key plutonium-production facilities under monitoring, while the United States and partners would provide heavy fuel oil, two proliferation-resistant light-water reactors, and steps toward political and economic normalization (Arms Control Association, 2022; Sigal, 1997). In absolute-payoff terms, compliance promised material benefits to North Korea (energy assistance and improved external relations) while reducing proliferation risk for the U.S. and regional allies. Yet the arrangement unraveled, and by 2003 North Korea announced withdrawal from the non-proliferation treaty, explicitly framing its decision in security terms (Kirgis, 2003).

Read through a relative-gains lens, this trajectory is consistent with the Scodel–Minas H4 pattern: even when cooperation appears strictly advantageous in absolute terms, it can fail when leaders weight relative security position and vulnerability. Analysts have emphasized that North Korea treated its nuclear option as bargaining leverage and that the regime has come to view nuclear capability as central to deterrence and regime survival, helping explain why it accepted severe diplomatic and economic costs rather than lock in a cooperative equilibrium that left it strategically dependent on rivals (Howell, 2020; Sigal, 1997).

If the H4 findings had been part of the standard toolkit of game theory courses and experimental-economics surveys, both the collapse of the Agreed Framework and the realist arguments of the 1980s might have looked less like a challenge to the economic model and more like a natural extension of existing experimental evidence. Scholars might have pointed to Scodel and Minas as early laboratory confirmation that actors sometimes defect from efficient agreements to avoid relative disadvantage, even when absolute payoffs rise. The “mystery” of failed win–win treaties would then be historically reframed: not as a surprising deviation from Nash-based cooperation, but as a macro-level manifestation of motives already visible in small-scale laboratory games.

4.3. Ultimatum Rejections and the Missing Experimental Lineage

The ultimatum game has arguably become the canonical classroom example of an anomaly for standard game theory. Following Güth et al. (1982) and later popularizations such as Thaler (1988), rejections of low offers are often introduced as prima facie evidence that people are willing to sacrifice money to enforce fairness norms. This framing has been extremely influential, shaping both the behavioral-economics canon and broader public discussions of human rationality.

Again, a counterfactual historical perspective suggests a different narrative. The behavior of responders who reject highly unequal offers—preferring zero to a small positive payoff that leaves them far behind the proposer—is structurally similar to the Scodel–Minas subjects who chose competitive actions in H4. In both cases, actors accept absolute losses to avoid or reduce large negative payoff differences. The key difference is that ultimatum experiments emerged in the early 1980s, two decades after Scodel and Minas, and in an economics context that did not routinely cite the earlier conflict-research literature.

This similarity can be made more tangible by writing the responder’s decision as a choice between an unequal but positive payoff vector and a zero vector. If the proposer offers a small share $\epsilon$ to the responder, acceptance yields $(1-\epsilon ,\epsilon )$ while rejection yields $(0,0)$. Under purely absolute utility, $\epsilon >0$ implies acceptance. Under a utility mapping that includes disadvantageous inequality, however, acceptance can generate a sufficiently large disutility term from being far behind, making rejection the preferred response (Bolton & Ockenfels, 2000; Fehr & Schmidt, 1999). The responder’s rejection is then not irrational; it is the selection of an action that eliminates an unfavorable payoff difference, even at a cost in absolute income.

Seen this way, the ultimatum game contains an H4-style structure. In H4, a cooperator facing a defector receives $(1,3)$: a strictly positive absolute payoff coupled with a large negative payoff difference. Choosing the competitive action, or accepting mutual defection, can be understood as an attempt to avoid being left behind, just as rejection in ultimatum bargaining avoids accepting an outcome in which the opponent is vastly ahead. The mapping is, therefore, not merely rhetorical: both settings can be represented by the same kind of transformed-payoff logic in which interpersonal comparison changes what is defined as a “best” response.

Had there been a continuous experimental lineage from the non-zero-sum games of the 1950s and 1960s to the ultimatum literature of the 1980s and 1990s, low-offer rejections might have been framed less as a shock to game theory and more as another instance of a familiar pattern: people resist strongly disadvantageous outcomes, even at a cost. Experimental economists might still have drawn the same lessons about fairness and social preferences, but their descriptive claims about the novelty of the evidence would likely have been tempered. The fact that the ultimatum game was seen as a “surprise” is, on this view, partly a consequence of the earlier experimental tradition having been forgotten.

Taken together, these three cases suggest that the puzzle status of altruistic punishment, failed win–win treaties, and ultimatum rejections is historically contingent. When viewed through the lens of Scodel and Minas, each behavior appears less as an unexpected anomaly and more as a reappearance, in new guises and domains, of a relative-payoff logic already documented in the early years of experimental game research.

5. Discussion and Conclusions

The Scodel–Minas experiments offer an early empirical glimpse of how deeply relative payoffs shape strategic behavior. Long before the rise of behavioral economics and evolutionary game theory, their subjects behaved as if both absolute gains and relative standing mattered, with the latter often decisive when the two came into conflict. Game H4 crystallizes this pattern by showing that even when cooperation is both a strict best response and a Pareto optimum, many individuals choose to defect in order to avoid being outperformed.

Seen through the lens of evolutionary dynamics, this is exactly what one should expect. In both biological and cultural evolution, strategies spread when they earn higher payoffs than competitors, not when they maximize some absolute standard (Maynard Smith, 1982; Nowak, 2006; Weibull, 1995). Relative-payoff concerns create incentives for pre-emptive defection and punishment that are invisible in purely Nash-based analyses.

From a historical perspective, this helps to reinterpret the status of later “puzzles” in the evolution of cooperation. Altruistic punishers, recalcitrant states, and ultimatum responders who reject positive offers were indeed surprising to many economists in the 1980s and 1990s, given the then-dominant models of self-interest and absolute utility (Fehr & Gächter, 2002; Grieco, 1988; Güth et al., 1982; Henrich et al., 2001; Snidal, 1991; Thaler, 1988). However, if the Scodel–Minas findings had been part of the standard experimental canon, these behaviors might have been seen less as anomalies and more as further instances of an already-recognized pattern: actors trade off absolute gains against relative position in predictable ways. In that counterfactual history, the contribution of later work would have been to generalize and formalize the relative-payoff logic, rather than to discover it anew.

For contemporary theory and policy, the main lesson is straightforward. Equilibrium concepts that ignore relative payoffs risk mischaracterizing both the stability of cooperation and the sources of defection. Analyses and institutions that focus exclusively on absolute gains may, therefore, be systematically over-optimistic about the prospects for cooperation. International treaties, corporate incentive schemes, and domestic policy reforms often assume that actors will accept any arrangement that leaves them better off in absolute terms. The evidence from Scodel and Minas, from altruistic punishment and ultimatum bargaining, and from international-relations research on relative gains all point in the same direction: relative payoffs matter (Bolton & Ockenfels, 2000; Fehr & Schmidt, 1999; Grieco, 1988; Shutters, 2009, 2016; Snidal, 1991). Designing robust cooperative institutions, therefore, requires attention not only to efficiency but also to the distribution of benefits and the perceived fairness of outcomes.

Historically, the neglect of the Scodel–Minas experiments illustrates how disciplinary boundaries can delay recognition of important results (Crane, 1972; Kuhn, 1962/1970). Because they published in a conflict-resolution venue rather than a core economics journal, their work did not enter the canonical accounts of experimental or evolutionary game theory. Recovering their contribution enriches the history of economic thought by showing that key empirical challenges to Nash-based reasoning were visible in the laboratory well before the behavioral and evolutionary turns.