|
on Game Theory |
| By: | Anand, Kartik; König, Philipp Johann |
| Abstract: | This article provides a practical overview for applying the global games approach to solve models with multiple equilibria that are often used in discussions on fi- nancial and macroprudential policies. Global games offer a tractable approach to resolve multiple equilibria by introducing incomplete information, thereby yield- ing unique equilibrium predictions. The article proceeds along the lines of a simple regime change game with strategic complementarities. Starting from the canonical regime change game with homogeneous players, it extends the discus- sion to include heterogeneous groups of players and interlinkages across different institutions with different sets of players. These extensions highlight not only how strategic complementarities can amplify fragility across players and institu- tions but also how heterogeneity and interlinkages affects the design of micro- and macroprudential policy interventions. Finally, the article briefly discusses the application of global games to dynamic coordination games. |
| Keywords: | Global Games, Multiple Equilibria, Coordination Games |
| JEL: | C72 D82 G01 |
| Date: | 2026 |
| URL: | https://d.repec.org/n?u=RePEc:zbw:bubdps:337465 |
| By: | Gill, David (Purdue University); Rosokha, Yaroslav (Purdue University) |
| Abstract: | In this paper, we identify level-k reasoning in repeated games that operates at the level of a supergame strategy, rather than at the level of individual rounds. First, we develop a model of level-k reasoning that incorporates choices over strategies as well as beliefs about strategies chosen by others. Then, using data from the Indefinitely Repeated Prisoner's Dilemma that includes elicited strategies and beliefs about strategies, we classify a substantial fraction of subjects as level-1 or level-2. Moreover, we show that when level-k reasoning operates at the level of a strategy, cognitive ability and experience both predict higher level reasoning. |
| Keywords: | Level-k, repeated game, Prisoner’s Dilemma, strategy, beliefs, cognitive ability, experience, elicitation, bounded rationality, experiment, game theory JEL Classification: C73, D83, D91 |
| Date: | 2026 |
| URL: | https://d.repec.org/n?u=RePEc:cge:wacage:788 |
| By: | Andrei Iakovlev |
| Abstract: | When multiple informative equilibria are possible in a general cheap talk game, how much information can a principal guarantee herself? To answer this question, I define the notion of worst-case implementation-implementation via the worst non-trivial equilibrium of a mechanism. Under this objective, standard full-commitment mechanisms fail, yielding the principal no more than her no-communication payoff. Partial commitment, however, can provide a strict improvement. The possibility of facing a strategic, uncommitted principal disciplines the agent's reporting incentives across all equilibria. I characterize the worst-case optimal mechanism and payoff under weak assumptions on the players' preferences. The optimal mechanism has a simple two-message structure. The agent's messages are polarizing, designed to maximize their strategic impact on the uncommitted principal's actions. If full commitment is interpreted as decision automation, these results highlight a fundamental complementarity between automated and human decision-makers: the presence of a human aligns the agent's incentives to reveal information, while the automated system leverages these informative reports to take accurate actions. This strategic interaction is often overlooked by literature that compares the two based on standalone decision accuracy. Applications of the model include bail-setting automation, fintech lending, delegation, lobbying, and audit design. |
| Date: | 2026–02 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2602.13645 |
| By: | Buhai, Ioan-Sebastian (Stockholm University - SOFI, UC Chile - Instituto de Economia, and University of Minho - NIPE) |
| Abstract: | Wage dispersion and job-to-job mobility are central features of modern labour markets, yet canonical equilibrium search models with exogenous job ladders struggle to account for both facts and the magnitude of frictional wage inequality. We develop a continuous-time equilibrium search model in which match surplus follows a diffusion, workers choose on-the-job search and separation, firms post state-contingent wages, and the cross-sectional distribution of match states endogenously pins down outside options and the job ladder. The problem is formulated as a stationary mean field game with a one-dimensional surplus state. We establish existence and uniqueness of stationary equilibrium under standard regularity and monotonicity conditions, and show that separation is governed by a free-boundary rule. Quantitatively, we solve the coupled Hamilton-Jacobi-Bellman & Kolmogorov system with monotone finite-difference methods, calibrate the model to micro evidence on match productivity and mobility, and use it to decompose wage dispersion and to study how firing costs, search subsidies, and volatility shape mobility, the job ladder, and the wage distribution. |
| Keywords: | wage dispersion, on-the-job search, job ladders, stochastic match productivity, mean field games |
| JEL: | C73 D83 J31 J63 J64 |
| Date: | 2026–02 |
| URL: | https://d.repec.org/n?u=RePEc:iza:izadps:dp18358 |
| By: | Sarah Necker; Benoit Le Maux |
| Abstract: | We examine how absolute and relative gains within reward schemes influence dishonesty. In our online experiment, we vary two payoff dimensions in a cheating mind game: the payoff level and the absolute payoff difference between being successful or not. A higher payoff level has a negative impact on dishonesty, while a greater absolute payoff difference has a positive impact. Variations in these dimensions also affect the relative payoff difference: we observe the largest decrease in dishonesty when moving from the highest to the lowest relative gain. A potential implication is that reward schemes with a reasonable amount from low performance and a relatively small bonus from high performance are least prone to cheating, and this can be achieved in a cost-neutral way. |
| Keywords: | dishonesty, mind game, cheating, payoffs, incentive schemes, bonus |
| JEL: | C91 C92 M52 J28 J33 |
| Date: | 2026 |
| URL: | https://d.repec.org/n?u=RePEc:ces:ceswps:_12481 |
| By: | Nemanja Antic; Harry Pei |
| Abstract: | We develop an overlapping generations model where each agent observes a verifiable private signal about the state and, with positive probability, also receives signals disclosed by his predecessor. The agent then takes an action and decides which signals to pass on. Each agent's action has a positive externality on his predecessor and his optimal action increases in his belief about the state. We show that as the communication friction vanishes, agents become increasingly selective in disclosing information. As the probability that messages reach the next generation approaches one, all signals except those with the highest likelihood ratio will be concealed in equilibrium. |
| Date: | 2026–02 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2602.09406 |
| By: | Amann, Erwin; Alyousuf, Manar |
| Abstract: | We develop a population game with heterogeneous infection-loss types and social-circle mediated prosociality, where altruists internalize expected infection losses within a setting-specific circle. Equilibrium admits closed-form cutoff rules and an aggregate non-vaccination rate that reduces to two composites: a private-cost pressure ratio and an altruistic-concern index combining altruist prevalence with circle structure. A utilitarian planner yields a socially optimal cutoff; we characterize when circle-mediated altruism is welfare-improving versus welfare-excessive, implying under- or over-vaccination. We embed subsidies, prosocial pledges, and indirect pressure as primitives and obtain closed-form comparative statics and interaction effects: pledges are marginal substitutes for subsidies and pressure, while subsidies and pressure are marginal complements. Policy leverage is greatest in high-contact, high-vulnerability settings, where calibrated norm-based interventions with modest transfers can dominate stringent pressure or large subsidies. |
| Abstract: | Wir analysieren Impfentscheidungen in einem Populationsspiel, in dem Individuen sowohl in ihren erwarteten Infektionsverlusten als auch in ihren sozialen Motiven heterogen sind. Das Gleichgewicht ist durch monotone Schwellenregeln charakterisiert. Die aggregierte Impfquote lässt sich auf zwei zusammenfassende Kenngrößen zurückführen: den Privatkostendruck sowie ein Prosozialgewicht, welches den Anteil prosozialer Individuen und Sozialkreisstruktur bündelt. Es wird gezeigt, unter welchen Bedingungen prosoziale Internalisierung zu Unter- oder Überimpfung im Vergleich zum gesellschaftlichen Optimum führt. Anschließend werden drei politikrelevante Instrumente untersucht: finanzielle Zuschüsse, normbasierte Selbstbindung und indirekter Druck. Wir leiten geschlossene komparativ-statische Effekte und Interaktionen ab, identifizieren Substitutions- und Komplementaritätsbeziehungen zwischen den Instrumenten und zeigen, dass normbasierte Selbstbindung abnehmende Grenzwirkungen aufweist. Daraus folgen klare Gestaltungsregeln für zielgerichtete und abgestimmte Maßnahmen, insbesondere in Umgebungen mit hoher Kontaktintensität und hoher Vulnerabilität. |
| Keywords: | Vaccination games, Altruism, Prosocial preferences, Externalities, Population games, Social circles, Policy design, Crowding out, Heterogeneity |
| JEL: | C72 D64 I18 |
| Date: | 2026 |
| URL: | https://d.repec.org/n?u=RePEc:zbw:rwirep:337491 |
| By: | Brian Roberson |
| Abstract: | We study incentive design when multiple principals simultaneously design mechanisms for their respective teams in environments with strategic spillovers. In this environment, each principal's set of incentive-compatible mechanisms--those that satisfy their own agents' incentive compatibility constraints--depends on the mechanisms offered by the other teams. Following a classic example by Myerson (1982), such games may lack equilibrium due to discontinuities in the correspondence of incentive-compatible mechanisms. We establish general conditions for equilibrium existence by introducing a novel approach that involves tracking both the outcome distributions along the truthful-obedient path and the sets of outcome distributions achievable through unilateral deviations, thereby providing a foundation for analyzing a wide range of multi-principal mechanism design with team production and agency problems. |
| Date: | 2026–02 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2602.20281 |
| By: | Tim J. Boonen; Kenneth Tsz Hin Ng; Tak Wa Ng; Thai Nguyen |
| Abstract: | We propose a peer-to-peer (P2P) insurance scheme comprising a risk-sharing pool and a reinsurer. A plan manager determines how risks are allocated among members and ceded to the reinsurer, while the reinsurer sets the reinsurance loading. Our work focuses on the strategic interaction between the plan manager and the reinsurer, and this focus leads to two game-theoretic contract designs: a Pareto design and a Bowley design, for which we derive closed-form optimal contracts. In the Pareto design, cooperation between the reinsurer and the plan manager leads to multiple Pareto-optimal contracts, which are further refined by introducing the notion of coalitional stability. In contrast, the Bowley design yields a unique optimal contract through a leader-follower framework, and we provide a rigorous verification of the individual rationality constraints via pointwise comparisons of payoff vectors. Comparing the two designs, we prove that the Bowley-optimal contract is never Pareto optimal and typically yields lower total welfare. In our numerical examples, the presence of reinsurance improves welfare, especially with Pareto designs and a less risk-averse reinsurer. We further analyze the impact of the single-loading restriction, which disproportionately favors members with riskier losses. |
| Date: | 2026–02 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2602.14223 |
| By: | Joshua Bißbort; Daniel Heyen; Soheil Shayegh |
| Abstract: | Advice plays a central role in health, personal finance, and energy-efficiency decisions. We study how a benevolent expert should design verifiable advice—such as whether to commission a diagnostic test of different accuracy—when the agent is behaviorally biased, either neglecting payoff-relevant considerations or updating beliefs in a systematic, non-Bayesian way. The expert both informs the agent about underlying risk and persuades the agent away from choices driven by bias. In a Bayesian persuasion framework with a binary safe-versus-risky decision and moderate (monotone) distortions, we show that the expert’s payoff need not be monotone in informativeness: intermediate information can reduce welfare relative to no information. Nonetheless, full disclosure remains optimal. |
| Keywords: | expert advice, risky choice, Bayesian persuasion, information design, behavioral bias, non-Bayesian updating, full disclosure |
| JEL: | D82 D81 D03 D83 I18 |
| Date: | 2026 |
| URL: | https://d.repec.org/n?u=RePEc:ces:ceswps:_12482 |
| By: | Corneo, Giacomo |
| Abstract: | NATO enlargement and Russian annexation of Crimea marked crucial turning points. According to one narrative, the Russian occupation was part of a plan to re-establish dominion over Eastern Europe. According to a rival view, it was an attempt to counter a U.S. plan to subjugate Russia. I scrutinize the logical requirements of those narratives in a multi-stage game of incomplete information that produces equilibrium play such that first NATO is enlarged and then Russia attacks Ukraine. The two competing narratives correspond to two different separating equilibria. Conditions for their existence inform about the consistency and plausibility of the associated narratives. |
| Keywords: | Ukraine war, NATO enlargement, incomplete information |
| JEL: | H8 N4 Z1 |
| Date: | 2026 |
| URL: | https://d.repec.org/n?u=RePEc:zbw:fubsbe:337470 |
| By: | Cheaheon Lim |
| Abstract: | This paper develops a theory of learning under ambiguity induced by the decision maker's beliefs about the collection of data correlated with the true state of the world. Within our framework, two classical results on Bayesian learning extend to the setting with ambiguity: experiments are equivalent to distributions over posterior beliefs, and Blackwell's more informative and more valuable orders coincide. When applied to the setting of robust Bayesian analysis, our results clarify the source of time inconsistency in the Gamma-minimax problem and provide an argument in favor of the conditional Gamma-minimax criterion. We also apply our results to a persuasion game to illustrate that our model provides a natural benchmark for communication under ambiguity. |
| Date: | 2026–02 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2602.07634 |
| By: | Cecilia Carvalho; Nicolas Goulart; Daniel Monte; Emanuel Ornelas |
| Abstract: | We study the sustainability of international trading rules in a multipolar world. A rules-based equilibrium is shaped by three forces. A static temptation to exploit market power undermines cooperation, while two dynamic forces support it: the efficiency gains from rules and the cost of reestablishing the regime once a country becomes hegemonic. When multipolarity is short-lived and involves few co-leaders, a strong enough prospect of future hegemony ensures rules cooperation. However, in a more fragmented world, the sustainability of rules is more likely if shared leadership is expected to persist, to ensure long-lasting efficiency gains. |
| Keywords: | hegemonic stability theory, World Trade Organization, trade agreements, multipolarity |
| JEL: | F02 F13 F53 H87 |
| Date: | 2026 |
| URL: | https://d.repec.org/n?u=RePEc:ces:ceswps:_12395 |
| By: | Federico Echenique (UC Berkeley - University of California [Berkeley] - UC - University of California); Matías Núñez (CREST - Centre de Recherche en Économie et Statistique - ENSAI - Ecole Nationale de la Statistique et de l'Analyse de l'Information [Bruz] - Groupe ENSAE-ENSAI - Groupe des Écoles Nationales d'Économie et Statistique - X - École polytechnique - IP Paris - Institut Polytechnique de Paris - ENSAE Paris - École Nationale de la Statistique et de l'Administration Économique - Groupe ENSAE-ENSAI - Groupe des Écoles Nationales d'Économie et Statistique - IP Paris - Institut Polytechnique de Paris - CNRS - Centre National de la Recherche Scientifique) |
| Abstract: | We describe a sequential mechanism that fully implements the set of efficient outcomes in environments with quasi-linear utilities. The mechanism asks agents to take turns in defining prices for each outcome, with a final player choosing an outcome for all: Price & Choose. The choice triggers a sequence of payments, from each agent to the preceding agent. We present several extensions. First, payoff inequalities may be reduced by endogenizing the order of play. Second, our results extend to a model without quasi-linear utility, to a setting with an outside option, robustness to max-min behavior and caps on prices. |
| Keywords: | Prices, Mechanism, Subgame-perfect implementation, Efficiency |
| Date: | 2025–05–01 |
| URL: | https://d.repec.org/n?u=RePEc:hal:journl:hal-05511714 |
| By: | Zhihao Tang; Shixin Wang |
| Abstract: | In practice, auction data are often endogenously censored and anonymous, revealing only limited outcome statistics rather than full bid profiles. We study robust auction design when the seller observes only aggregated, anonymous order statistics and seeks to maximize worst-case expected revenue over all product distributions consistent with the observed statistic. We show that simple and widely used mechanisms are robustly optimal. Specifically, posted pricing is robustly optimal given the distribution of the highest value; the Myerson auction designed for the unique consistent i.i.d. distribution is robustly optimal given the lowest value distribution; and the second-price auction with an optimal reserve is robustly optimal when an intermediate order statistic is observed and the implied i.i.d. distribution is regular above its reserve. More generally, for a broad class of monotone symmetric mechanisms depending only on the top k order statistics, including multi-unit and position auctions, the worst-case revenue is attained under the i.i.d. distribution consistent with the observed k-th order statistic. Our results provide a tractable foundation for non-discriminatory auction design, where fairness and privacy are intrinsic consequences of the information structure rather than imposed constraints. |
| Date: | 2026–02 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2602.20429 |
| By: | Ian Ball; Deniz Kattwinkel; Jan Knoepfle |
| Abstract: | Two horizontally differentiated firms compete for consumers who are partially informed about their future preferences. The firms screen consumers by offering menus of option contracts. Each consumer enters contracts with both firms. Subsequently, each consumer learns his preferences and purchases only one product. We find the unique equilibrium. Relative to spot pricing, consumption is distorted because each consumer is endogenously locked into one firm. If contracting is sufficiently early, so that consumers are less informed and hence less differentiated, consumers benefit; this reverses the conclusion in the monopoly case. Exclusive contracting further benefits consumers by intensifying competition. |
| Date: | 2026–02 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2602.08144 |
| By: | Manik Dhar; Kunal Mittal; Clayton Thomas |
| Abstract: | Among two-candidate elections that treat the candidates symmetrically and never result in a tie, which voting rules are fair? A natural requirement is that each voter exerts an equal influence over the outcome, i.e., is equally likely to swing the election one way or the other. A voter's influence has been formalized in two canonical ways: the Shapley-Shubik (1954) index and the Banzhaf (1964) index. We consider both indices, and ask: Which electorate sizes admit a fair voting rule (under the respective index)? For an odd number $n$ of voters, simple majority rule is an example of a fair voting rule. However, when $n$ is even, fair voting rules can be challenging to identify, and a diverse literature has studied this problem under different notions of fairness. Our main results completely characterize which values of $n$ admit fair voting rules under the two canonical indices we consider. For the Shapley-Shubik index, a fair voting rule exists for $n>1$ if and only if $n$ is not a power of $2$. For the Banzhaf index, a fair voting rule exists for all $n$ except $2$, $4$, and $8$. Along the way, we show how the Shapley-Shubik and Banzhaf indices relate to the winning coalitions of the voting rule, and compare these indices to previously considered notions of fairness. |
| Date: | 2026–02 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2602.13894 |
| By: | Kan Kuno |
| Abstract: | This paper studies bargaining when buyers can continue searching for alternative sellers while negotiating, which limits their commitment to complete a transaction. Using transaction level data from a Japanese online marketplace, I document frequent post-agreement nonpurchase and show that buyers who explicitly pledge immediate payment are more likely to have their offers accepted, renege less often, and complete transactions faster. I develop and estimate a dynamic bargaining model with buyer search and limited commitment. Counterfactuals that restrict search during bargaining show that increased buyer commitment can reduce total welfare. Sellers especially those with higher valuations benefit from the elimination of delays and walkaways and respond by raising list prices. This reduces buyer welfare by lowering the option value of search and increasing expected list prices. Platform revenue also declines because buyer behavior shifts away from counteroffers and negotiated prices fall. |
| Date: | 2026–02 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2602.13707 |