Pub Date : 2026-03-01Epub Date: 2026-01-16DOI: 10.1016/j.geb.2026.01.003
Hyukjun Kwon , Ran I. Shorrer
We study priority-based matching markets. We propose a novel partial order for comparing matching mechanisms in terms of their “fairness.” Using this order, we show that efficiency-adjusted deferred acceptance (EADA) is justified-envy minimal in the class of efficient mechanisms, while top trading cycles (TTC) and other popular mechanisms are not. Our findings highlight EADA as an interesting alternative to TTC in the context of transplantation-organ markets. Restricting attention to strategyproof mechanisms, we show that TTC is justified-envy minimal, providing robustness to the result of Abdulkadiroğlu et al. (2020).
{"title":"Justified-envy-minimal efficient mechanisms for priority-based matching","authors":"Hyukjun Kwon , Ran I. Shorrer","doi":"10.1016/j.geb.2026.01.003","DOIUrl":"10.1016/j.geb.2026.01.003","url":null,"abstract":"<div><div>We study priority-based matching markets. We propose a novel partial order for comparing matching mechanisms in terms of their “fairness.” Using this order, we show that efficiency-adjusted deferred acceptance (EADA) is justified-envy minimal in the class of efficient mechanisms, while top trading cycles (TTC) and other popular mechanisms are not. Our findings highlight EADA as an interesting alternative to TTC in the context of transplantation-organ markets. Restricting attention to strategyproof mechanisms, we show that TTC is justified-envy minimal, providing robustness to the result of Abdulkadiroğlu et al. (2020).</div></div>","PeriodicalId":48291,"journal":{"name":"Games and Economic Behavior","volume":"157 ","pages":"Pages 71-87"},"PeriodicalIF":1.0,"publicationDate":"2026-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146079350","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"经济学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
In this paper, we introduce a novel equilibrium concept, called the equilibrium cycle, which seeks to capture the outcome of oscillatory game dynamics. Unlike the (pure) Nash equilibrium, which defines a fixed point of mutual best responses, an equilibrium cycle is a set-valued solution concept that can be demonstrated even in games where best responses do not exist (for example, in discontinuous games). The equilibrium cycle identifies a Cartesian product set of action profiles that satisfies three important properties: stability against external deviations, instability against internal deviations, and minimality. This set-valued equilibrium concept generalizes the classical notion of the minimal curb set to discontinuous games. In finite games, the equilibrium cycle is related to strongly connected sink components of the best response graph.
{"title":"Equilibrium cycle: A “Dynamic” equilibrium","authors":"Tushar Shankar Walunj , Shiksha Singhal , Veeraruna Kavitha , Jayakrishnan Nair","doi":"10.1016/j.geb.2026.02.007","DOIUrl":"10.1016/j.geb.2026.02.007","url":null,"abstract":"<div><div>In this paper, we introduce a novel equilibrium concept, called the equilibrium cycle, which seeks to capture the outcome of oscillatory game dynamics. Unlike the (pure) Nash equilibrium, which defines a fixed point of mutual best responses, an equilibrium cycle is a set-valued solution concept that can be demonstrated even in games where best responses do not exist (for example, in discontinuous games). The equilibrium cycle identifies a Cartesian product set of action profiles that satisfies three important properties: <em>stability</em> against external deviations, <em>instability</em> against internal deviations, and <em>minimality</em>. This set-valued equilibrium concept generalizes the classical notion of the minimal curb set to discontinuous games. In finite games, the equilibrium cycle is related to strongly connected sink components of the best response graph.</div></div>","PeriodicalId":48291,"journal":{"name":"Games and Economic Behavior","volume":"157 ","pages":"Pages 286-297"},"PeriodicalIF":1.0,"publicationDate":"2026-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147384944","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"经济学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2026-03-01Epub Date: 2026-02-20DOI: 10.1016/j.geb.2026.02.006
Robert Bredereck , Jiehua Chen , Dušan Knop , Junjie Luo , Rolf Niedermeier
Adaptivity to changing environments and constraints is key to success in modern society. We address this principle by proposing “incrementalized versions” of Stable Marriage and Stable Roommates, asking what the computational cost is of adapting an existing stable matching after agents’ preferences have changed. We additionally require that the new stable matching should not deviate too much from the old one. After formalizing these incremental versions, we provide a comprehensive computational complexity landscape of Incremental Stable Marriage and Incremental Stable Roommates. To this end, we exploit the parameters “degree of change” in the input (difference between old and new preference profile) and in the output (difference between old and new stable matching). We obtain both hardness and tractability results. In particular, with ties in preferences, both problems remain computationally intractable even under minimal preference changes, whereas with strict preferences, both become (fixed-parameter) tractable, regardless of the extent of preference changes.
{"title":"Adapting stable matchings to evolving preferences","authors":"Robert Bredereck , Jiehua Chen , Dušan Knop , Junjie Luo , Rolf Niedermeier","doi":"10.1016/j.geb.2026.02.006","DOIUrl":"10.1016/j.geb.2026.02.006","url":null,"abstract":"<div><div>Adaptivity to changing environments and constraints is key to success in modern society. We address this principle by proposing “incrementalized versions” of <span>Stable Marriage</span> and <span>Stable Roommates</span>, asking what the computational cost is of adapting an existing stable matching after agents’ preferences have changed. We additionally require that the new stable matching should not deviate too much from the old one. After formalizing these incremental versions, we provide a comprehensive computational complexity landscape of <span>Incremental Stable Marriage</span> and <span>Incremental Stable Roommates</span>. To this end, we exploit the parameters “degree of change” in the input (difference between old and new preference profile) and in the output (difference between old and new stable matching). We obtain both hardness and tractability results. In particular, with ties in preferences, both problems remain computationally intractable even under minimal preference changes, whereas with strict preferences, both become (fixed-parameter) tractable, regardless of the extent of preference changes.</div></div>","PeriodicalId":48291,"journal":{"name":"Games and Economic Behavior","volume":"157 ","pages":"Pages 322-350"},"PeriodicalIF":1.0,"publicationDate":"2026-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147384946","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"经济学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2026-03-01Epub Date: 2026-01-23DOI: 10.1016/j.geb.2026.01.005
Enrico Diecidue , Thomas Langer , Sven Nolte , Sebastian Riedmiller , Judith C. Schneider
In a series of three experiments, we investigate intrinsic preferences for timing and skewness of information resolution in a “compound lottery” (CL) and “information structure” (IS) environment. In the first experiment, we rule out predeterminedness of the outcome, i.e., realization before making the decision, as a driver of different timing preferences between the environments. In the second experiment, we show that skewness preferences in a two-outcome setting differ between the two environments. In the third comprehensive experiment, we integrate all three dimensions (timing, skewness, and environment) into a three-outcome setting, which allows a rigorous treatment of skewness. With respect to timing, participants prefer to receive information early in both environments. In case of a gradual resolution, participants strictly prefer positively skewed information in the IS environment, but symmetric information in the CL environment. Our results show that skewness and environment must be jointly taken into account when studying preferences for information resolution.
{"title":"Timing and skewness of information revelation: Evidence on information structures and compound lotteries","authors":"Enrico Diecidue , Thomas Langer , Sven Nolte , Sebastian Riedmiller , Judith C. Schneider","doi":"10.1016/j.geb.2026.01.005","DOIUrl":"10.1016/j.geb.2026.01.005","url":null,"abstract":"<div><div>In a series of three experiments, we investigate intrinsic preferences for timing and skewness of information resolution in a “compound lottery” (CL) and “information structure” (IS) environment. In the first experiment, we rule out predeterminedness of the outcome, i.e., realization before making the decision, as a driver of different timing preferences between the environments. In the second experiment, we show that skewness preferences in a two-outcome setting differ between the two environments. In the third comprehensive experiment, we integrate all three dimensions (timing, skewness, and environment) into a three-outcome setting, which allows a rigorous treatment of skewness. With respect to timing, participants prefer to receive information early in both environments. In case of a gradual resolution, participants strictly prefer positively skewed information in the IS environment, but symmetric information in the CL environment. Our results show that skewness and environment must be jointly taken into account when studying preferences for information resolution.</div></div>","PeriodicalId":48291,"journal":{"name":"Games and Economic Behavior","volume":"157 ","pages":"Pages 109-124"},"PeriodicalIF":1.0,"publicationDate":"2026-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146079349","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"经济学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2026-03-01Epub Date: 2025-11-07DOI: 10.1016/j.geb.2025.10.010
Marcus Roel , Zhuoqiong Chen
This paper examines behavioral differences in sequential games that arise when choices are elicited via the direct-response method, where players observe the choices made by those who acted earlier and respond with a single choice, or strategy method, where they make their choice(s) in response to all possible choices by those who acted before regardless of whether such actions were taken. We conducted a 2 × 2 between-subject large-scale online experiment with over 8000 participants on Amazon MTurk, manipulating both the elicitation method and participants’ ex-ante beliefs about player 1’s choices via an information-provision treatment. In neutrally framed binary-choice games, a sequential Prisoners’ Dilemma and a mini-Ultimatum Game, we document that the strategy method does not appear to alter player 2’s preferences, i.e., their tendency to reward cooperation or reject unfair offers. However, it reduces the tendency to reward defection and reject fair offers, which we interpret as a reduction in mistakes.
{"title":"Strategy vs. direct-response method: evidence from a large online experiment on simple social dilemmas","authors":"Marcus Roel , Zhuoqiong Chen","doi":"10.1016/j.geb.2025.10.010","DOIUrl":"10.1016/j.geb.2025.10.010","url":null,"abstract":"<div><div>This paper examines behavioral differences in sequential games that arise when choices are elicited via the direct-response method, where players observe the choices made by those who acted earlier and respond with a single choice, or strategy method, where they make their choice(s) in response to all possible choices by those who acted before regardless of whether such actions were taken. We conducted a 2 × 2 between-subject large-scale online experiment with over 8000 participants on Amazon MTurk, manipulating both the elicitation method and participants’ ex-ante beliefs about player 1’s choices via an information-provision treatment. In neutrally framed binary-choice games, a sequential Prisoners’ Dilemma and a mini-Ultimatum Game, we document that the strategy method does not appear to alter player 2’s preferences, i.e., their tendency to reward cooperation or reject unfair offers. However, it reduces the tendency to reward defection and reject fair offers, which we interpret as a reduction in mistakes.</div></div>","PeriodicalId":48291,"journal":{"name":"Games and Economic Behavior","volume":"157 ","pages":"Pages 153-185"},"PeriodicalIF":1.0,"publicationDate":"2026-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147385137","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"经济学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2026-03-01Epub Date: 2026-02-11DOI: 10.1016/j.geb.2026.02.001
Sung-Ha Hwang , Youngwoo Koh , Sosung Baik
We study the optimal auction design problem when bidders are ambiguity averse and follow the max-min expected utility model. Each bidder’s set of priors consists of beliefs that are close to the seller’s belief, where “closeness” is defined by a divergence. For a given allocation rule, we show that optimal transfers belong to a specific class of transfers, termed win-lose dependent transfers, in which bidders’ transfers upon winning and losing depend only on their own types but not on their opponents’ type reports. This result effectively reduces the infinite-dimensional problem of identifying an optimal transfer function into a two-dimensional problem of determining two constants-one for winning and another for losing. Solving this reduced problem, we show that among efficient mechanisms without transfers to losing bidders, the first-price auction is optimal, thereby outperforming other auction formats such as the second-price auction. We also discuss how the structure of the set of priors is related to the revenue ranking between the first- and second-price auctions.
{"title":"Auction design with ambiguity: Optimality of the first-price auction","authors":"Sung-Ha Hwang , Youngwoo Koh , Sosung Baik","doi":"10.1016/j.geb.2026.02.001","DOIUrl":"10.1016/j.geb.2026.02.001","url":null,"abstract":"<div><div>We study the optimal auction design problem when bidders are ambiguity averse and follow the max-min expected utility model. Each bidder’s set of priors consists of beliefs that are close to the seller’s belief, where “closeness” is defined by a divergence. For a given allocation rule, we show that optimal transfers belong to a specific class of transfers, termed <em>win-lose dependent transfers,</em> in which bidders’ transfers upon winning and losing depend only on their own types but not on their opponents’ type reports. This result effectively reduces the infinite-dimensional problem of identifying an optimal transfer function into a two-dimensional problem of determining two constants-one for winning and another for losing. Solving this reduced problem, we show that among efficient mechanisms without transfers to losing bidders, the first-price auction is optimal, thereby outperforming other auction formats such as the second-price auction. We also discuss how the structure of the set of priors is related to the revenue ranking between the first- and second-price auctions.</div></div>","PeriodicalId":48291,"journal":{"name":"Games and Economic Behavior","volume":"157 ","pages":"Pages 298-321"},"PeriodicalIF":1.0,"publicationDate":"2026-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147384945","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"经济学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2026-03-01Epub Date: 2026-02-18DOI: 10.1016/j.geb.2026.02.005
Yotam Gafni , Aviv Yaish
To allocate transactions to blocks, cryptocurrencies use auction-esque transaction fee mechanisms (TFMs). A conjecture of Roughgarden (2024) asks whether there is a TFM that is incentive compatible for both users and the miner and is also resistant to a collusion that allows them to jointly increase overall welfare. We resolve this question in the negative for deterministic TFMs, through a comprehensive characterization of designs robust to this form of collusion. For randomized TFMs, we show limits on the efficiency they can achieve.
{"title":"Transaction fee mechanisms robust to welfare-increasing collusion","authors":"Yotam Gafni , Aviv Yaish","doi":"10.1016/j.geb.2026.02.005","DOIUrl":"10.1016/j.geb.2026.02.005","url":null,"abstract":"<div><div>To allocate transactions to blocks, cryptocurrencies use auction-esque <em>transaction fee mechanisms (TFMs)</em>. A conjecture of Roughgarden (2024) asks whether there is a TFM that is incentive compatible for both users and the miner and is also resistant to a collusion that allows them to jointly increase overall welfare. We resolve this question in the negative for deterministic TFMs, through a comprehensive characterization of designs robust to this form of collusion. For randomized TFMs, we show limits on the efficiency they can achieve.</div></div>","PeriodicalId":48291,"journal":{"name":"Games and Economic Behavior","volume":"157 ","pages":"Pages 351-375"},"PeriodicalIF":1.0,"publicationDate":"2026-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147384991","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"经济学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2026-03-01Epub Date: 2025-12-04DOI: 10.1016/j.geb.2025.11.012
Álvaro Cartea , Patrick Chang , José Penalva , Harrison Waldon
We prove a Folk theorem when players with bounded rationality learn as they play a repeated potential game. We use a dynamic generalization of smooth fictitious play with bounded m-recall strategies to model learning with bounded rationality that is consistent with learning by algorithms. In a repeated potential game with perfect monitoring, we use this learning model to show that for any feasible and individually rational payoff profile, if players have sufficient recall, are sufficiently patient, and best respond with sufficiently few mistakes, then the players have a non-zero probability of learning an m-recall strategy profile that achieves an average payoff close to the specified payoff profile for an appropriate continuation game. Moreover, the strategy profile learned is an m-recall ϵ-subgame perfect equilibrium of the repeated game. This finding demonstrates that competition authorities are correct in their concern about algorithmic collusion.
{"title":"Algorithmic collusion and a folk theorem from learning with bounded rationality","authors":"Álvaro Cartea , Patrick Chang , José Penalva , Harrison Waldon","doi":"10.1016/j.geb.2025.11.012","DOIUrl":"10.1016/j.geb.2025.11.012","url":null,"abstract":"<div><div>We prove a Folk theorem when players with bounded rationality learn as they play a repeated potential game. We use a dynamic generalization of smooth fictitious play with bounded <em>m</em>-recall strategies to model learning with bounded rationality that is consistent with learning by algorithms. In a repeated potential game with perfect monitoring, we use this learning model to show that for any feasible and individually rational payoff profile, if players have sufficient recall, are sufficiently patient, and best respond with sufficiently few mistakes, then the players have a non-zero probability of learning an <em>m</em>-recall strategy profile that achieves an average payoff close to the specified payoff profile for an appropriate continuation game. Moreover, the strategy profile learned is an <em>m</em>-recall ϵ-subgame perfect equilibrium of the repeated game. This finding demonstrates that competition authorities are correct in their concern about algorithmic collusion.</div></div>","PeriodicalId":48291,"journal":{"name":"Games and Economic Behavior","volume":"157 ","pages":"Pages 1-21"},"PeriodicalIF":1.0,"publicationDate":"2026-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145950324","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"经济学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2026-03-01Epub Date: 2026-02-03DOI: 10.1016/j.geb.2026.01.010
Guilherme Carmona, Krittanai Laohakunakorn
We consider a setting where each player of a simultaneous-move game privately designs an information structure before playing the game. One of these information structures is chosen at random to determine the distribution of the private messages that players receive. These messages allow players to correlate their actions; however, their private design implies a push from correlated to Nash equilibria. Indeed, the sequential equilibrium payoffs of the extensive-form game with privately designed information structures are correlated equilibrium payoffs of the underlying simultaneous-move game, but not all correlated equilibrium payoffs are sequential equilibrium payoffs. In generic 2-player games, the latter are specific convex combinations of two Nash equilibrium payoffs.
{"title":"Privately designed correlated equilibrium","authors":"Guilherme Carmona, Krittanai Laohakunakorn","doi":"10.1016/j.geb.2026.01.010","DOIUrl":"10.1016/j.geb.2026.01.010","url":null,"abstract":"<div><div>We consider a setting where each player of a simultaneous-move game privately designs an information structure before playing the game. One of these information structures is chosen at random to determine the distribution of the private messages that players receive. These messages allow players to correlate their actions; however, their private design implies a push from correlated to Nash equilibria. Indeed, the sequential equilibrium payoffs of the extensive-form game with privately designed information structures are correlated equilibrium payoffs of the underlying simultaneous-move game, but not all correlated equilibrium payoffs are sequential equilibrium payoffs. In generic 2-player games, the latter are specific convex combinations of two Nash equilibrium payoffs.</div></div>","PeriodicalId":48291,"journal":{"name":"Games and Economic Behavior","volume":"157 ","pages":"Pages 237-252"},"PeriodicalIF":1.0,"publicationDate":"2026-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147384942","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"经济学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2026-03-01Epub Date: 2026-01-25DOI: 10.1016/j.geb.2026.01.006
Ioannis Anagnostides , Fivos Kalogiannis , Ioannis Panageas , Emmanouil-Vasileios Vlatakis-Gkaragkounis , Stephen Mcaleer
Adversarial team games model multiplayer strategic interactions in which a team of identically-interested players is competing against an adversarial player in a zero-sum game. Such games capture many well-studied settings in game theory, such as congestion games, but go well-beyond to environments wherein the cooperation of one team—in the absence of explicit communication—is obstructed by competing entities; the latter setting remains poorly understood despite its numerous applications. Since the seminal work of Von Stengel and Koller (GEB ‘97), different solution concepts have received attention from an algorithmic standpoint. Yet, the complexity of the standard Nash equilibrium has remained open.
In this paper, we settle this question by showing that computing a Nash equilibrium in adversarial team games belongs to the class continuous local search (CLS), thereby establishing CLS-completeness by virtue of the recent CLS-hardness result of Rubinstein and Babichenko (STOC ‘21) in potential games. To do so, we leverage linear programming duality to prove that any ϵ-approximate stationary strategy for the team can be extended in polynomial time to an O(ϵ)-approximate Nash equilibrium, where the O( · ) notation suppresses polynomial factors. As a consequence, we show that the Moreau envelope of a suitable best response function acts as a potential under certain natural gradient-based dynamics.
{"title":"Algorithms and complexity for computing Nash equilibria in adversarial team games","authors":"Ioannis Anagnostides , Fivos Kalogiannis , Ioannis Panageas , Emmanouil-Vasileios Vlatakis-Gkaragkounis , Stephen Mcaleer","doi":"10.1016/j.geb.2026.01.006","DOIUrl":"10.1016/j.geb.2026.01.006","url":null,"abstract":"<div><div><em>Adversarial team games</em> model multiplayer strategic interactions in which a team of identically-interested players is competing against an adversarial player in a zero-sum game. Such games capture many well-studied settings in game theory, such as congestion games, but go well-beyond to environments wherein the cooperation of one team—in the absence of explicit communication—is obstructed by competing entities; the latter setting remains poorly understood despite its numerous applications. Since the seminal work of Von Stengel and Koller (GEB ‘97), different solution concepts have received attention from an algorithmic standpoint. Yet, the complexity of the standard Nash equilibrium has remained open.</div><div>In this paper, we settle this question by showing that computing a Nash equilibrium in adversarial team games belongs to the class <em>continuous local search (</em><strong>CLS</strong><em>)</em>, thereby establishing <strong>CLS</strong>-completeness by virtue of the recent <strong>CLS</strong>-hardness result of Rubinstein and Babichenko (STOC ‘21) in potential games. To do so, we leverage linear programming duality to prove that any ϵ-approximate stationary strategy for the team can be extended in polynomial time to an <em>O</em>(ϵ)-approximate Nash equilibrium, where the <em>O</em>( · ) notation suppresses polynomial factors. As a consequence, we show that the <em>Moreau envelope</em> of a suitable best response function acts as a <em>potential</em> under certain natural gradient-based dynamics.</div></div>","PeriodicalId":48291,"journal":{"name":"Games and Economic Behavior","volume":"157 ","pages":"Pages 138-152"},"PeriodicalIF":1.0,"publicationDate":"2026-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147385030","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"经济学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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