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Spatial Competition Across Borders: The Role of Patients’ Mobility and Institutional Settings
Equilibrium Coalition Structures in Three-Player Symmetric Games
The Raiffa–Kalai–Smorodinsky Solution as a Mechanism for Dividing the Uncertain Future Profit of a Partnership
The Impact of Gifts and Shared Experiences on an Investor-Manager Relationship

Journal Description

Games

Games is a scholarly, peer-reviewed, open access journal of studies on game theory and its applications published bimonthly online by MDPI.

Open Access— free for readers, with article processing charges (APC) paid by authors or their institutions.
High Visibility: indexed within Scopus, ESCI (Web of Science), MathSciNet, zbMATH, RePEc, EconLit, EconBiz, and other databases.
Rapid Publication: manuscripts are peer-reviewed and a first decision is provided to authors approximately 32.6 days after submission; acceptance to publication is undertaken in 6.9 days (median values for papers published in this journal in the first half of 2025).
Recognition of Reviewers: reviewers who provide timely, thorough peer-review reports receive vouchers entitling them to a discount on the APC of their next publication in any MDPI journal, in appreciation of the work done.

Impact Factor: 0.5 (2024)

Imprint Information Journal Flyer Open Access ISSN: 2073-4336

Latest Articles

64 pages, 2132 KB

Open AccessFeature PaperArticle

Test Me If You Can—Providing Optimal Information for Consumers Through a Novel Certification Mechanism

by Ulrike Vollstädt, Patrick Imcke, Franziska Brendel and Christiane Ehses-Friedrich

Games 2025, 16(5), 44; https://doi.org/10.3390/g16050044 (registering DOI) - 29 Aug 2025

Certifiers such as Stiftung Warentest (Germany), Which? (UK), and Consumer Reports (US) reduce asymmetric information between buyers and sellers by providing credible information about product quality. However, due to their limited testing capacities, they face a set selection problem and test only a [...] Read more.

Certifiers such as Stiftung Warentest (Germany), Which? (UK), and Consumer Reports (US) reduce asymmetric information between buyers and sellers by providing credible information about product quality. However, due to their limited testing capacities, they face a set selection problem and test only a subset of all available product models. We show theoretically that, under any current mechanism to select product models for testing, buyers always end up buying suboptimal product models, unless all product models which would be sold under complete information (or all but the overall cheapest one) happen to be tested. Instead, we propose a novel mechanism based on voluntary disclosure, but with the same testing capacity, which always yields the maximum possible consumer surplus and thus weakly dominates any current mechanism. Furthermore, we confirm in a controlled laboratory experiment that our mechanism significantly increases consumer surplus. Full article

20 pages, 592 KB

Open AccessArticle

The Power of Passivity in the Hirshleifer Contest Under Small Noise

by Guang-Zhen Sun

Games 2025, 16(5), 43; https://doi.org/10.3390/g16050043 - 29 Aug 2025

Hirshleifer’s difference-form contest technology is a useful tool in the study of a class of conflict, especially military combats. We aim to highlight an important feature that the Hirshleifer contest model distinctively has, namely passivity (bidding zero effort) may stand as an effective [...] Read more.

Hirshleifer’s difference-form contest technology is a useful tool in the study of a class of conflict, especially military combats. We aim to highlight an important feature that the Hirshleifer contest model distinctively has, namely passivity (bidding zero effort) may stand as an effective choice in conflict even when the contest is highly deterministic (i.e., with small noise). For that purpose, we establish two propositions on the contest with

n \geq 2

risk-neutral contestants under small noise. The first proposition states that every contestant bids arbitrarily close to zero (if not bidding zero with positive probability at all) under sufficiently small noise. The second proposition, more strikingly, states that every contestant either bids arbitrarily close to the second-highest valuation (among all the contestants’ valuations), or simply remains passive with certainty under any sufficiently small noise. We further show that the first proposition holds for the contest between risk-averse individuals endowed with constant absolute risk aversion as well, and illustrate by an example how quickly polarization in bidding among contestants, as is predicted by the propositions, may emerge as the noise of the contest abates. These results help pave the way toward a complete characterization of the difference-form contest. Full article

(This article belongs to the Section Applied Game Theory)

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21 pages, 493 KB

Open AccessFeature PaperArticle

A Theoretical Analysis of Cooperation Incentives for Non-Mutually Dependent Sellers

by Lorenzo Ferrari, Werner Güth, Vittorio Larocca and Luca Panaccione

Games 2025, 16(5), 42; https://doi.org/10.3390/g16050042 - 27 Aug 2025

This paper examines stochastic cooperation in markets with two sellers who exhibit one-sided dependency. The independent seller’s pricing influences the dependent seller’s demand, but not vice versa. We study the one-dimensional hybrid game class whose parameter is the exogenously given probability of cooperation. [...] Read more.

This paper examines stochastic cooperation in markets with two sellers who exhibit one-sided dependency. The independent seller’s pricing influences the dependent seller’s demand, but not vice versa. We study the one-dimensional hybrid game class whose parameter is the exogenously given probability of cooperation. In each game of this class, both sellers simultaneously choose prices that determine their endogenous threats, i.e., conflict profits. The sellers are aware of the cooperation probability but cannot condition prices on whether or not there is cooperation. We characterize the equilibrium prices and the sellers’ expected profits. Our main result shows that the independent seller earns higher expected profits when cooperation is more likely. In contrast, the dependent seller earns lower expected profits when the likelihood of cooperation is below a threshold that we characterize explicitly, and higher profits are earned thereafter. These findings suggest that, within our framework, antitrust concerns may be mitigated. Since dependent sellers can incur losses from cooperation, collusion attempts become less viable in markets with one-sided dependency. Full article

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23 pages, 380 KB

Open AccessArticle

Power Indices with Threats in Precoalitions

by Jochen Staudacher

Games 2025, 16(5), 41; https://doi.org/10.3390/g16050041 - 25 Aug 2025

We investigate power indices for simple games with precoalitions which distribute power among players in an external and an internal step. We extend an existing approach which uses the Public Good index both on the external level in the quotient game as well [...] Read more.

We investigate power indices for simple games with precoalitions which distribute power among players in an external and an internal step. We extend an existing approach which uses the Public Good index both on the external level in the quotient game as well as on the internal level for measuring the leverage of players to threaten their peers through departing the precoalition. We replace the Public Good index in that model by five other efficient power indices, i.e., the Shapley–Shubik index, the Deegan–Packel index, the Johnston index and two indices based on null player free winning coalitions. Axiomatizations of the novel power indices with threat partitions are presented. We also propose a slight modification to the existing framework for threat power indices which guarantees that null players are always assigned zero power. Numerical results for all power indices combined with different threat partitions are presented and discussed. Full article

(This article belongs to the Section Cooperative Game Theory and Bargaining)

10 pages, 526 KB

Open AccessArticle

Cooperative and Non-Cooperative Strategies in Product Warranty Pricing: A Hierarchical Game Approach

by Henrique Santos and Thyago Nepomuceno

Games 2025, 16(4), 40; https://doi.org/10.3390/g16040040 - 13 Aug 2025

This paper analyzes the pricing dynamics of product warranties by developing a three-player hierarchical game model involving a manufacturer, an independent service agent, and a consumer. The model provides a scenario where the manufacturer and the agent form a coalition to coordinate pricing [...] Read more.

This paper analyzes the pricing dynamics of product warranties by developing a three-player hierarchical game model involving a manufacturer, an independent service agent, and a consumer. The model provides a scenario where the manufacturer and the agent form a coalition to coordinate pricing strategies, while interacting non-cooperatively with the consumer. In this framework, the manufacturer sets the product’s sale price, including the base warranty, while the agent determines the price of extended maintenance services. The key contribution is the application of the Shapley value to equitably distribute the coalition’s profits based on each member’s contribution—a novel approach in the warranty pricing literature. We detail the characteristic functions that define the coalition’s structure and present computer simulations to estimate the expected costs associated with maintenance services. A comprehensive sensitivity analysis is applied to report how changes in parameters influence equilibrium strategies and players’ payoffs. The results provide strategic insights into how manufacturers and agents can coordinate to optimize pricing, capture consumer surplus, and improve decision-making in warranty service markets. Full article

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14 pages, 784 KB

Open AccessArticle

Non-Cooperative Representations of Cooperative Games

by Justin Chan

Games 2025, 16(4), 39; https://doi.org/10.3390/g16040039 - 8 Aug 2025

Non-cooperative games in normal form are specified by a player set, sets of player strategies, and payoff functions. Cooperative games, meanwhile, are specified by a player set and a worth function that maps coalitions of players to payoffs they can feasibly achieve. Although [...] Read more.

Non-cooperative games in normal form are specified by a player set, sets of player strategies, and payoff functions. Cooperative games, meanwhile, are specified by a player set and a worth function that maps coalitions of players to payoffs they can feasibly achieve. Although these games study distinct aspects of social behavior, this paper proposes a novel attempt at relating the two models. In particular, cooperative games may be represented by a non-cooperative game in which players can freely sign binding agreements to form coalitions. These coalitions inherit a joint strategy set and seek to maximize collective payoffs. When these coalitions play against one another, the equilibrium payoffs for each coalition coincide with what is predicted by the worth function. This paper proves sufficient conditions under which cooperative games can be represented by non-cooperative games. This paper finds that all strictly superadditive partition function form (PFF) games can be represented under Nash equilibrium (NE) and rationalizability; that all weakly superadditive characteristic function form (CFF) games can be represented under NE; and that all weakly superadditive PFF games can be represented under trembling hand perfect equilibrium (THPE). Full article

(This article belongs to the Section Cooperative Game Theory and Bargaining)

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24 pages, 526 KB

Open AccessArticle

Responsibility Hoarding by Overconfident Managers

by Petra Nieken, Abdolkarim Sadrieh and Nannan Zhou

Games 2025, 16(4), 38; https://doi.org/10.3390/g16040038 - 26 Jul 2025

Overconfidence is a well-established behavioral bias that involves the overestimation of one’s own capabilities. We introduce a model in which managers and agents exert effort in a joint production, after the manager decides on the allocation of the tasks. A rational manager tends [...] Read more.

Overconfidence is a well-established behavioral bias that involves the overestimation of one’s own capabilities. We introduce a model in which managers and agents exert effort in a joint production, after the manager decides on the allocation of the tasks. A rational manager tends to reduce their own effort by delegating the critical task to the agent more often than in an efficient task allocation. In contrast, an overconfident manager engages in responsibility hoarding, i.e., is likely to delegate a critical task less often to the agent than a rational manager. In fact, a manager with a sufficiently high ability and a moderate degree of overconfidence increases the total welfare by refusing to delegate critical tasks and by exerting more effort than a rational manager. Finally, we derive the conditions under which the responsibility hoarding can persist in an organization, showing that the bias survives as long as the overconfident manager can rationalize the observed output by underestimating the ability of the agent. Full article

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31 pages, 883 KB

Open AccessArticle

Pure Bayesian Nash Equilibria for Bayesian Games with Multidimensional Vector Types and Linear Payoffs

by Sébastien Huot and Abbas Edalat

Games 2025, 16(4), 37; https://doi.org/10.3390/g16040037 - 14 Jul 2025

In this work, we study n-agent Bayesian games with m-dimensional vector types and linear payoffs, also called linear multidimensional Bayesian games. This class of games is equivalent with n-agent, m-game uniform multigames. We distinguish between games that have a [...] Read more.

In this work, we study n-agent Bayesian games with m-dimensional vector types and linear payoffs, also called linear multidimensional Bayesian games. This class of games is equivalent with n-agent, m-game uniform multigames. We distinguish between games that have a discrete type space and those with a continuous type space. More specifically, we are interested in the existence of pure Bayesian Nash equilibriums for such games and efficient algorithms to find them. For continuous priors, we suggest a methodology to perform Nash equilibrium searches in simple cases. For discrete priors, we present algorithms that can handle two-action and two-player games efficiently. We introduce the core concept of threshold strategy and, under some mild conditions, we show that these games have at least one pure Bayesian Nash equilibrium. We illustrate our results with several examples like the double-game prisoner’s dilemma (DGPD), the game of chicken, and the sustainable adoption decision problem (SADP). Full article

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33 pages, 3140 KB

Open AccessArticle

“Anything Goes” in an Ultimatum Game?

by Peter Paul Vanderschraaf

Games 2025, 16(4), 36; https://doi.org/10.3390/g16040036 - 9 Jul 2025

I consider an underexplored possible explainer of the “surprising” results of Ultimatum Game experiments, namely, that Proposers and Recipients consider following only some of all the logically possible strategies of their Ultimatum Game. I present an evolutionary analysis of different games having the [...] Read more.

I consider an underexplored possible explainer of the “surprising” results of Ultimatum Game experiments, namely, that Proposers and Recipients consider following only some of all the logically possible strategies of their Ultimatum Game. I present an evolutionary analysis of different games having the same set of allowable Proposer offers and functions that determine Proposer and Recipient payoffs. For Unrestricted Ultimatum Games, where Recipients may choose from among any of the logically possible pure strategies, populations tend to evolve most often to Nash equilibria where Proposers make the lowest allowable offer. However, for Threshold Reduced Ultimatum Games, where Recipients must choose from among minimum acceptable offer strategies, and for Range Reduced Ultimatum Games, where Recipients must choose from among pure strategies that spurn offers that are “too high” as well as “too low”, populations tend to evolve most often to Nash equilibria where Proposers offer substantially more than the lowest possible offer, a result that is consistent with existing Ultimatum Game experimental results. Finally, I argue that, practically speaking, actual Proposers and Recipients will likely regard some reduction of the Unrestricted Ultimatum Game as their game because, for them, the strategies of this reduction are salient. Full article

(This article belongs to the Special Issue Evolution of Cooperation and Evolutionary Game Theory)

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17 pages, 329 KB

Open AccessArticle

Pool Formation with Three Patent Owners

by Hao Liu, Xuewen Qian, Chen Qu and Jingyi Shen

Games 2025, 16(4), 35; https://doi.org/10.3390/g16040035 - 8 Jul 2025

We analyze the endogenous formation of patent pools among three patent owners and the associated welfare effects. Under a condition of synergistic three-patent combination, either a unique symmetric equilibrium or infinitely many asymmetric equilibria can arise when patents are fragmented. By using the [...] Read more.

We analyze the endogenous formation of patent pools among three patent owners and the associated welfare effects. Under a condition of synergistic three-patent combination, either a unique symmetric equilibrium or infinitely many asymmetric equilibria can arise when patents are fragmented. By using the notion of equilibrium binding agreements, we show that (1) when there is a unique symmetric equilibrium under fragmented patents, the complete pool is both stable and welfare-maximizing; (2) fragmented patents are stable in the presence of infinitely many asymmetric equilibria; and (3) when considering only a single specific asymmetric equilibrium under fragmented patents, the complete pool is welfare-maximizing if it is stable, while fragmented patents can be both stable and welfare-maximizing under certain conditions. We also discuss an alternative version of synergism and an alternative bargaining protocol for patent pool formation. Full article

(This article belongs to the Section Cooperative Game Theory and Bargaining)

24 pages, 468 KB

Open AccessArticle

Hierarchies and Promotions in Political Institutions: Accountability and Selection

by B. Pablo Montagnes, Stephane Wolton and Junyan Jiang

Games 2025, 16(4), 34; https://doi.org/10.3390/g16040034 - 4 Jul 2025

Hierarchies are common in political settings. From judges to elected politicians, as well as from activists to bureaucrats, political agents compete for promotion to higher positions. This paper studies political tournaments and their impact on two aspects of political performance: accountability and selection. [...] Read more.

Hierarchies are common in political settings. From judges to elected politicians, as well as from activists to bureaucrats, political agents compete for promotion to higher positions. This paper studies political tournaments and their impact on two aspects of political performance: accountability and selection. While larger tournaments discourage effort, they improve selection. We also discuss the optimal design of tournaments as a function of the principal’s objectives and the features of the environment. We find that tournaments of size two (such as two-candidate elections) are generally suboptimal. Our analysis also highlights that increased desirability of promotion always increases effort but can reduce the optimal tournament size under certain conditions. We also present a range of other comparative statics. Full article

(This article belongs to the Special Issue Conflict and Communication: Applications of Game Theory to Political Economy)

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13 pages, 596 KB

Open AccessArticle

Nonmarket Valuation by Contests Under Two American Rules: A Game-Theoretic Analysis

by Sung-Hoon Park and Jason F. Shogren

Games 2025, 16(4), 33; https://doi.org/10.3390/g16040033 - 30 Jun 2025

Herein, we further examine how we can value nonmarket goods and services by considering the costs associated with environmental conflicts. Focusing on two American rules—the asymmetric reimbursement system and the contingent fee contract—we develop a strategic game-theoretic model in which a citizens group [...] Read more.

Herein, we further examine how we can value nonmarket goods and services by considering the costs associated with environmental conflicts. Focusing on two American rules—the asymmetric reimbursement system and the contingent fee contract—we develop a strategic game-theoretic model in which a citizens group engages a delegate through a contingent fee compensation contract, while a polluter engages a delegate through an hourly fee compensation contract. If the citizens group prevails, the polluter is obligated to contribute a portion of the contingent fee. Solving for the subgame perfect equilibrium, two results emerge. First, the 4x-rule can be maintained through the adjustment of the asymmetric reimbursement system. Second, the asymmetric reimbursement system can serve both as a supplementary method to measure nonmarket valuation and to reduce the rent dissipation resulting from environmental conflicts under general circumstances. Full article

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16 pages, 336 KB

Open AccessArticle

The Impact of Market Mood on a Dynamic Model of Insider Trading

by Ruohan Wang, Jing Wang and Zhi Yang

Games 2025, 16(4), 32; https://doi.org/10.3390/g16040032 - 20 Jun 2025

According to the research, the proportions of various types of investors may or may not change in response to different trading strategies or complex trading environments. This paper investigates a single-period trading model for multiple risk-averse and risk-neutral insider traders. The distinction is [...] Read more.

According to the research, the proportions of various types of investors may or may not change in response to different trading strategies or complex trading environments. This paper investigates a single-period trading model for multiple risk-averse and risk-neutral insider traders. The distinction is that we consider the impact of the number of risk-averse traders and different types of insider traders on market liquidity. The model contains four types of trading entities: risk-neutral and risk-adverse insider traders, risk-neutral market makers, and noise traders. Firstly, we prove the existence and uniqueness of the model’s linear Nash equilibrium; secondly, we compare the model with multiple risk-neutral and risk-adverse insider traders in the market to the model with only risk-neutral insider traders and risk-adverse insider traders. It is shown that the market liquidity parameter

λ

decreases with the increase in the number of risk-averse persons

N_{2}

in a particular range and increases with the increase in the number of risk-averse persons

N_{2}

in another range. Markets with risk-neutral and risk-averse insider traders have consistently lower liquidity than markets with only risk-neutral insider traders. Comparing this to markets with only risk-adverse insider traders reveals that the number of risk-adverse traders heavily influences market liquidity. Full article

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20 pages, 336 KB

Open AccessArticle

Spatial Competition Across Borders: The Role of Patients’ Mobility and Institutional Settings

by Laura Levaggi and Rosella Levaggi

Games 2025, 16(3), 31; https://doi.org/10.3390/g16030031 - 5 Jun 2025

Health care systems rely on geographical boundaries that secure financial stability and adequate planning. Quality differences across regions often arise for efficiency reasons, causing patient flows if mobility is free. In this paper, a theoretical spatial competition model is developed to study the [...] Read more.

Health care systems rely on geographical boundaries that secure financial stability and adequate planning. Quality differences across regions often arise for efficiency reasons, causing patient flows if mobility is free. In this paper, a theoretical spatial competition model is developed to study the role of patients’ mobility on quality setting and to draw policy implications on its use as an instrument to reduce disparities, in a setting where regions differ in efficiency, costs, and market structure. From the analysis, it emerges that the institutional setting matters and a trade-off may appear between equity (in terms of quality difference across patients) and welfare (finding an allocation that maximizes social benefits). In a centralized setting, it is optimal to regulate mobility and increase the quality gap, while allowing free mobility calls for a refined quality setting, in which, depending on a balance between costs and benefits, the quality gap may be either increased or decreased. In decentralization the gap is generally lower, compared to centralization: the different consideration of benefits from local quality provision results in higher quality levels where the market structure is vertically integrated. Full article

(This article belongs to the Section Applied Game Theory)

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15 pages, 289 KB

Open AccessArticle

Equilibrium Coalition Structures in Three-Player Symmetric Games

by Jingyi Shen and Chen Qu

Games 2025, 16(3), 30; https://doi.org/10.3390/g16030030 - 5 Jun 2025

Cited by 1

In symmetric games with externalities across coalitions, we investigate how three players form coalitions using two solutions:

n^{*}

, which is a focal prediction of coalition structure in a class of noncooperative coalitional bargaining games, and equilibrium binding agreements, which represent the [...] Read more.

In symmetric games with externalities across coalitions, we investigate how three players form coalitions using two solutions:

n^{*}

, which is a focal prediction of coalition structure in a class of noncooperative coalitional bargaining games, and equilibrium binding agreements, which represent the cooperative blocking approach. We find that the coarsest equilibrium coalition structure (based on the latter notion) is never finer than

n^{*}

, and we provide a sufficient and necessary condition for these two solutions to generate the same coalition structure (i.e., the two solutions coincide if and only if the first coalition to form in

n^{*}

is not a two-player coalition or a particular condition about average coalitional worths is satisfied). In symmetric games with more than three players, we demonstrate through a series of examples that any relationship between these two solutions is possible. We also discuss symmetric games with positive externalities or equal division in which these two solutions coincide. Full article

13 pages, 836 KB

Open AccessFeature PaperArticle

The Raiffa–Kalai–Smorodinsky Solution as a Mechanism for Dividing the Uncertain Future Profit of a Partnership

by Yigal Gerchak and Eugene Khmelnitsky

Games 2025, 16(3), 29; https://doi.org/10.3390/g16030029 - 4 Jun 2025

Establishing a partnership necessitates agreeing on how to divide future profits or losses. We consider parties who wish to contract on the division of uncertain future profits. We propose to divide profits according to the Raiffa–Kalai–Smorodinsky (K-S) solution, which is the intersection point [...] Read more.

Establishing a partnership necessitates agreeing on how to divide future profits or losses. We consider parties who wish to contract on the division of uncertain future profits. We propose to divide profits according to the Raiffa–Kalai–Smorodinsky (K-S) solution, which is the intersection point of the feasible region’s boundary and the line connecting the disagreement and ideal points. It is the only function which satisfies invariance to linear transformations, symmetry, strong Pareto optimality, and monotonicity. We formulate the general problem of designing a contract which divides uncertain future profit between the partners and determines shares of each partner. We first focus on linear and, later, non-linear contracts between two partners, providing analytical and numerical solutions for various special cases in terms of the utility functions of the partners, their beliefs, and the disagreement point. We then generalize the analysis to any number of partners. We also consider a contract which is partially based on the parties’ financial contribution to the partnership, which have a positive impact on profit. Finally, we address asymmetric K-S solutions. K-S solutions are seen to be a useful predictor of the outcome of negotiations, similar to Nash’s bargaining solution. Full article

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39 pages, 3987 KB

Open AccessArticle

The Impact of Gifts and Shared Experiences on an Investor-Manager Relationship

by Maximilian Olaf Hoyer and Frans van Winden

Games 2025, 16(3), 28; https://doi.org/10.3390/g16030028 - 4 Jun 2025

This paper experimentally investigates the relationship between an investor and a project manager. Project managers choose from a pool of projects, the success probabilities of which are uncertain. Investors can change projects, but also have to change project managers if they want to [...] Read more.

This paper experimentally investigates the relationship between an investor and a project manager. Project managers choose from a pool of projects, the success probabilities of which are uncertain. Investors can change projects, but also have to change project managers if they want to do so. An additional joint project or a voluntary money transfer precedes their interaction. We hypothesize that investors favor projects of managers with whom they share positive experiences at that stage, even though these experiences do not provide any information about the subsequent project’s success probability. Interaction through a voluntary transfer plays a clear and significant role in the investors’ decision-making via bonding, whereas the influence of merely sharing a positive or negative experience proves more complex. Full article

(This article belongs to the Section Behavioral and Experimental Game Theory)

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12 pages, 218 KB

Open AccessArticle

Match Stability with a Costly and Flexible Number of Positions

by James Gilmore and David Porter

Games 2025, 16(3), 27; https://doi.org/10.3390/g16030027 - 21 May 2025

One of the main goals of two-sided matching mechanisms is to pair two groups of agents in a stable manner. Stability means that no pair of agents has an incentive to deviate from their assigned match. The outcome of such a match can [...] Read more.

One of the main goals of two-sided matching mechanisms is to pair two groups of agents in a stable manner. Stability means that no pair of agents has an incentive to deviate from their assigned match. The outcome of such a match can have significant consequences for the participants involved. Most existing research in this field assumes that the quotas of organizations are fixed and externally determined, which may not always be realistic. We introduce the concept of slot stability, which considers the possibility that organizations may want to adjust their quotas after the match process. To address this issue, we propose an algorithm that generates both stable and slot-stable matches by using flexible, endogenous quotas. Full article

37 pages, 498 KB

Open AccessArticle

A General Model of Bertrand–Edgeworth Duopoly

by Blake A. Allison and Jason J. Lepore

Games 2025, 16(3), 26; https://doi.org/10.3390/g16030026 - 19 May 2025

This paper studies a class of two-player all-pay contests with externalities that encompass a general version of duopoly price competition. This all-pay contest formulation puts little restriction on production technologies, demand, and demand rationing. There are two types of possible equilibria: In the [...] Read more.

This paper studies a class of two-player all-pay contests with externalities that encompass a general version of duopoly price competition. This all-pay contest formulation puts little restriction on production technologies, demand, and demand rationing. There are two types of possible equilibria: In the first type of equilibrium, the lower bound to pricing is the same for each firm, and the probability of any pricing tie above this price is zero. Each firm’s equilibrium expected profit is their monopoly profit at the lower bound price. In the second type of equilibrium, one firm prices at the lower bound of the other firm’s average cost and other firm prices according to a non-degenerate mixed strategy. This type of equilibrium can only occur if production technologies are sufficiently different across firms. We derive necessary and sufficient conditions for the existence of pure strategy equilibrium and use these conditions to demonstrate the fragility of deterministic outcomes in pricing games. Full article

36 pages, 447 KB

Open AccessFeature PaperArticle

Procedural Information as a “Game Changer” in School Choice

by Yoan Hermstrüwer

Games 2025, 16(3), 25; https://doi.org/10.3390/g16030025 - 12 May 2025

This article explores the impact of procedural information on the behavior of students under two school admission procedures commonly used in the US, the EU, and other jurisdictions: the Gale–Shapley mechanism and the Boston mechanism. In a lab experiment, I compare the impact [...] Read more.

This article explores the impact of procedural information on the behavior of students under two school admission procedures commonly used in the US, the EU, and other jurisdictions: the Gale–Shapley mechanism and the Boston mechanism. In a lab experiment, I compare the impact of information about the mechanism, information about individually optimal application strategies, and information about both. I find that strategic and full information increases truth-telling and stability under the Gale–Shapley mechanism. Under the Boston mechanism, however, the adoption of equilibrium strategies remains unaffected. Contrary to the prevailing assumptions in matching theory, the Boston mechanism improves perceived fairness. These results underscore the importance of procedural transparency and suggest that eliminating justified envy may not be sufficient to foster fairness and mitigate litigation risks. Full article

(This article belongs to the Section Behavioral and Experimental Game Theory)

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