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on Game Theory |
| By: | Ian Fligler |
| Abstract: | In strategic games such as the prisoner's dilemma, allowing players to make binding offers of utility transfers before play has been shown to alter incentives and potentially support cooperative outcomes. These preplay exchange mechanisms reshape payoffs by transferring utility while being contingent on actions; however, they typically require side payments that can reduce individual benefits relative to joint cooperation. In this paper, we extend the analysis to a finite $n$-player prisoner's dilemma with ordered strategy sets, defined such that any restriction of strategies by any subset of players still yields a prisoner's dilemma. To achieve a robust cooperative outcome that resists group deviations, we introduce a novel class of mechanisms: $\textit{losing contracts}$. Unlike transfer-based preplay mechanisms, losing contracts require players to irrevocably reduce their own utility if they defect, thereby aligning individual incentives with cooperation without inter-player payments. With appropriately chosen loss amounts, losing contracts induce joint cooperation as the unique strong Nash equilibrium in the modified game and in every restricted game within it, ensuring that cooperative incentives persist even under possible external constraints on strategy sets. We show that our contracts can be constructively defined, reducing the preplay stage to a simple and binary decision for each player: whether to sign the contract or not. Furthermore, if the losing contract is only executed when all players sign, signing is a strictly dominant strategy for all. Finally, we extend these results to certain public goods games. |
| Date: | 2026–04 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2604.22563 |
| By: | Igor Sloev; Gerasimos Lianos |
| Abstract: | This study investigates the properties and stability of the Multiplicative Kantian Equilibrium (MKE) in symmetric games. We first demonstrate that MKE lacks strategic equivalence: the Kantian best-response function is not invariant under monotonic strategy rescaling. This strategic non-equivalence implies that the choice of measurement scale - a subjective interpretation of the game - materially impacts equilibrium outcomes. Exploiting this non-equivalence, in a game where players may be Kantian or Nasher, we propose an efficient strategy rescaling that allows Kantians to neutralize the free-rider advantage of Nashers, while preserving Pareto-efficient outcomes among themselves. In a dynamic framework, we show that the subgame-perfect Nash equilibrium with endogenous choice of optimization type leads all players to prefer Kantian optimization over Nash optimization. In an evolutionary setup, we show that Kantian optimization is an evolutionarily stable strategy (ESS). Our results suggest that the inherent strategic non-equivalence of Kantian optimization provides a robust pathway to stable cooperation. |
| Date: | 2026–05 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2605.00692 |
| By: | Atulya Jain |
| Abstract: | We study a dynamic sender-receiver game in which the sender observes a state evolving according to a Markov chain but does not observe the receiver's action. Despite the absence of feedback, dynamic interaction partially restores commitment. We show that any equilibrium payoff of a persuasion model with partial commitment, where the sender can deviate to signaling policies that preserve the marginal distribution over messages, can be achieved as a uniform equilibrium payoff in the dynamic game. Moreover, any convex combination of such payoffs across message distributions can also be sustained. When the sender's payoff is state-independent, she achieves the Bayesian persuasion payoff. |
| Date: | 2026–04 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2604.26443 |
| By: | Michael Greinecker; Martin Meier; Konrad Podczeck |
| Abstract: | Sequential equilibrium is one of the most fundamental refinements of Nash equilibrium for games in extensive form. However, it is not defined for extensive-form games in which a player can choose among a continuum of actions. We define a class of infinite extensive form games in which information behaves continuously as a function of past actions and define a natural notion of sequential equilibrium for this class. Sequential equilibria exist in this class and refine Nash equilibria. In standard finite extensive-form games, our definition selects the same strategy profiles as the traditional notion of sequential equilibrium. |
| Date: | 2026–04 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2604.25784 |
| By: | Kirill Rudov; Fedor Sandomirskiy; Leeat Yariv |
| Abstract: | Correlated equilibria arise naturally when agents communicate or rely on intermediaries such as recommendation systems. We study when a given Nash equilibrium can be improved within the set of correlated equilibria for general objectives. Our key insight is a detail-free criterion: any Nash equilibrium with three or more randomizing agents is generically improvable. We refine this insight to specific classes of games and objectives, including Pareto and utilitarian welfare, and provide constructive methods to obtain improvements. Our findings underscore the ubiquity of improvable Nash equilibria and the crucial role of correlation in enhancing strategic outcomes. |
| Date: | 2026–04 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2604.27258 |
| By: | Xiaoyun Qiu; Yang Yu; Haifeng Xu |
| Abstract: | Benchmark hacking refers to tuning a machine learning model to score highly on certain evaluation criteria without improving true generalization or faithfully solving the intended problem. We study this phenomenon in a generic machine learning contest, where each contestant chooses two types of effort: creative effort that improves model capability as desired by the contest host, and mechanistic effort that only improves the model's fitness to the particular task in contest without contributing to true generalization. We establish the existence of a symmetric monotone pure strategy equilibrium in this competition game. It also provides a natural definition of benchmark hacking in this strategic context by comparing a player's equilibrium effort allocation to that of a single-agent baseline scenario. Under our definition, contestants with types below certain threshold (low types) always engage in benchmark hacking, whereas those above the threshold do not. Furthermore, we show that more skewed reward structures (favoring top-ranked contestants) can elicit more desirable contest outcomes. We also provide empirical evidence to support our theoretical predictions. |
| Date: | 2026–04 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2604.22230 |
| By: | Pablo D. Azar |
| Abstract: | Bayesian Persuasion assumes that a sender can commit ex ante to an information structure and then release the realized signal ex post. This paper asks when that commitment technology can itself be implemented. After observing the state, a sender who also observes the realized signal can suppress unfavorable draws even if every disclosed signal is verifiably correct. We define Receiver-Private Certified Bayesian Persuasion, a benchmark in which the receiver obtains the signal and a certificate of correct generation while the sender does not learn the realized branch of the experiment. The main theorem shows that this benchmark is equivalent in cryptographic power to secure two-party computation. Thus cryptography is not merely an implementation device for persuasion; when the sender must be prevented from changing the signal sent to the receiver, hiding the signal from the sender is necessary. In stress-test applications, the primitive removes ex post discretion over which realized disclosure reaches depositors. |
| Keywords: | Bayesian persuasion; stress testing; central bank communications |
| JEL: | D82 D83 G28 |
| Date: | 2026–05–01 |
| URL: | https://d.repec.org/n?u=RePEc:fip:fednsr:103177 |
| By: | Harold Houba (Vrije Universiteit Amsterdam); Roland Iwan Luttens (Vrije Universiteit Amsterdam) |
| Abstract: | We introduce the Jungle Edgeworth Box economy as an analytical framework to analyze bilateral conflict and examine the interplay between coercion and voluntary exchange. We characterize the set of equilibria in which no further coercion or voluntary exchange ccurs. By assuming that coercion precedes voluntary exchange, we characterize the set of quilibria of a Nash Negotiation Game, where coercion is interpreted as a threat from the stronger to the weaker agent. We conclude that the jungle allocation is rarely the correct snapshot of the economy after coercion is over and exchange, facilitated by effective property rights, is about to begin. |
| Keywords: | bilateral conflict, coercion, jungle, barter, Edgeworth box |
| JEL: | D61 K11 P48 |
| Date: | 2025–11–14 |
| URL: | https://d.repec.org/n?u=RePEc:tin:wpaper:20250064 |
| By: | Yuhao Fu; Nobuyuki Hanaki; Haitao Wang |
| Abstract: | Artificial intelligence increasingly participates in economic interactions not only as a tool, but also as an autonomous bargaining counterpart negotiating on behalf of firms, platforms, and consumers. Yet little is known about how humans respond psychologically and strategically when bargaining with such agents in dynamic settings. We study this question in a laboratory experiment using a three-stage alternating-offer bargaining game in which participants negotiate in real time with either another human or a GPT-based AI agent. We also introduce a human-beneficiary condition in which the AI agent’s earnings may affect another participant’s payment. Agreements are not reached earlier in human–human bargaining than in human–AI bargaining, but they are reached significantly earlier when the AI’s payoff has human consequences. Human proposers offer more to human opponents than to AI agents, whereas responders become significantly more willing to accept unfair AI offers when AI earnings may benefit another human. These findings suggest that fairness and reciprocity toward AI are weaker and more conditional than toward humans, but partially re-emerge when AI outcomes affect real people. The results have implications for the design of AI negotiation systems and broader human–AI economic interactions. |
| Date: | 2026–04 |
| URL: | https://d.repec.org/n?u=RePEc:dpr:wpaper:1311 |
| By: | Jonathan Shaki; Eden Hartman; Sarit Kraus; Yonatan Aumann |
| Abstract: | Large language models (LLMs) are increasingly used to provide instructions to many agents who interact with one another. Such shared reliance couples agents who appear to act independently: they may in fact be guided by a common model. This coupling can change the prospects for cooperation among agents with misaligned incentives. We study settings in which multiple LLMs each advise a population of clients who participate in instances of an underlying game, creating strategic interaction at the level of the LLMs themselves. This induces a meta-game among the LLMs, mediated through clients. We first analyze the one-shot setting, where shared instructions can change equilibrium behavior only when an LLM may influence more than one role in the same interaction; in such cases, cooperation may emerge, and the effect of client share can be beneficial, harmful, or non-monotone, depending on the base game. Our main result concerns the repeated setting. We prove a folk theorem for LLMs: despite indirect observation and the clients' inability to identify which LLM advised their opponents, all feasible and individually rational outcomes can be sustained as $\varepsilon$-equilibria. The result does not follow from the standard folk theorem and requires new proof techniques. Together, these results show that shared LLM guidance can sustain cooperation among populations of agents even when the underlying incentives are misaligned. |
| Date: | 2026–05 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2605.06525 |
| By: | Zhiming Feng |
| Abstract: | This paper develops a decomposition methodology for common agency games in which each principal's payoff depends on her own outcome and the agent's type, but not on rivals' outcomes. The key step reduces each principal's best-response problem to a standard screening problem defined over the agent's indirect utility -- the upper envelope of her payoff over rivals' offerings. Individually best-responding mechanisms then assemble into a pure-menu perfect Bayesian equilibrium when a compatibility condition (utility-preserving recombination) ensures aligned tie-breaking across principals. Under a non-indifference condition, the decomposition recovers all equilibria except those sustained by menu items that no type of the agent actually selects but which nevertheless discipline the rival's screening problem. When principals' payoffs depend on the full allocation profile, the decomposition adapts only under substantive regularity conditions on the agent's off-path choice behavior, one of which coincides with Luce's choice axiom. I apply the methodology to two settings. In a quadratic-loss delegation model, equilibria feature one principal offering a finite menu of discrete ``regimes'' while the other receives piecewise full delegation within each regime. In a competitive bundling duopoly under intrinsic common agency, the decomposition yields equilibria exhibiting market splitting, in which firms specialize in complementary bundles, and asymmetric equilibria with a take-it-or-leave-it base contract paired with a nested or tree menu of upgrades. |
| Date: | 2026–04 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2604.23971 |
| By: | Mingyang Liu; Gabriele Farina; Asuman Ozdaglar |
| Abstract: | Most familiar equilibrium concepts, such as Nash and correlated equilibrium, guarantee only that no single player can improve their utility by deviating unilaterally. They offer no guarantees against profitable coordinated deviations by coalitions. Although the literature proposes solution concepts that provide stability against multilateral deviations (\emph{e.g.}, strong Nash and coalition-proof equilibrium), these generally fail to exist. In this paper, we study an alternative solution concept that minimizes coalitional deviation incentives, rather than requiring them to vanish, and is therefore guaranteed to exist. Specifically, we focus on minimizing the average gain of a deviating coalition, and extend the framework to weighted-average and maximum-within-coalition gains. In contrast, the minimum-gain analogue is shown to be computationally intractable. For the average-gain and maximum-gain objectives, we prove a lower bound on the complexity of computing such an equilibrium and present an algorithm that matches this bound. Finally, we use our framework to solve the \emph{Exploitability Welfare Frontier} (EWF), the maximum attainable social welfare subject to a given exploitability (the maximum gain over all unilateral deviations). |
| Date: | 2026–04 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2604.28186 |
| By: | Navin Kartik; Elliot Lipnowski; Harry Pei |
| Abstract: | Does electoral replacement ensure that officeholders eventually act in voters’ interests? We study a reputational model of accountability. Voters observe incumbents’ performance and decide whether to replace them. Politicians may be “good” types who always exert effort or opportunists who may shirk. We find that good long-run outcomes are always attainable, though the mechanism and its robustness depend on economic conditions. In environments conducive to incentive provision, some equilibria feature sustained effort, yet others exhibit some long-run shirking. In the complementary case, opportunists are never fully disciplined, but selection dominates: every equilibrium eventually settles on a good politician, yielding permanent effort. |
| JEL: | C73 D72 D78 D82 D83 |
| Date: | 2026–04 |
| URL: | https://d.repec.org/n?u=RePEc:nbr:nberwo:35154 |
| By: | Pietro Dall'Ara |
| Abstract: | Coordination is an important aspect of innovative contexts, where: the more innovative a course of action, the more uncertain its outcome. To study the interplay of coordination and informational ``complexity'', I embed a beauty-contest game into a complex environment. I identify a new conformity phenomenon. This effect may push towards the exploration of unknown alternatives or constitute a status-quo bias, depending on the network structure of players' interactions. In an application, I show that an organization with decentralized authority can implement profit maximization in a sufficiently complex environment. |
| Date: | 2026–04 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2604.24757 |
| By: | Gomez, Rafael (University of Toronto); Bryson, Alex (University College London); Willman, Paul (London School of Economics) |
| Abstract: | We review the literature on trust and cooperation with application to labour-management relations. We begin with the neo-classical economic view of self-regarding individuals operating with perfect information and show that once one abandons the dyadic case with perfect information, cooperation deteriorates as group size increases and the probability of behavioural or perceptual error rises. We show that self-regarding models have no way of explaining cooperative outcomes between management and labour under typical conditions and lead to less optimal forms of non-cooperative strategic bargaining. By way of contrast, models of cooperation with other-regarding preferences and trust – drawn from behavioural economics, social psychological, economic sociology and industrial relations literatures – show that a high level of cooperation can be attained even in large groups, with modest informational requirements, and that conditions allowing the evolution of trust and other-regarding social preferences are plausible and find empirical support. We also show that actors’ perceptions of the employment relationship underpin assumptions of human nature, which is what inevitably determines strategies used in labour-management relations. |
| Keywords: | trust, cooperation, labor-management relations |
| JEL: | J5 J53 |
| Date: | 2026–04 |
| URL: | https://d.repec.org/n?u=RePEc:iza:izadps:dp18577 |
| By: | Fernando E. Alvarez; Francisco J. Buera; Nicholas Trachter |
| Abstract: | We study optimal policy in a dynamic general equilibrium model where heterogeneous monopolistic competitive firms pay a fixed cost to adopt a frontier technology that grows exogenously. Using Mean Field Games tools, we show that the optimal policy consists of exactly two time-invariant subsidies: one correcting the static misallocation from market power, and one correcting the dynamic under-incentive to adopt. This holds outside of balanced growth paths, for any initial distribution of technology gaps. We analyze a simplified version of the model that aggregates to a Neoclassical Growth Model with an S-shaped production function whenever complementarities are strong, and fully characterize when the optimal policy uniquely implements the first best. When it does not, two novel results emerge: the efficient allocation prescribes escaping a poverty trap—providing an explicit optimality foundation for a Big Push—and, more surprisingly, escaping an abundance trap, where dismantling adopted technologies is optimal. In both cases, a temporary, costless supplementary policy restores unique implementation. |
| JEL: | D92 O14 O25 O40 |
| Date: | 2026–04 |
| URL: | https://d.repec.org/n?u=RePEc:nbr:nberwo:35133 |
| By: | Andre, Peter; Heidhues, Paul; Kőszegi, Botond; Murooka, Takeshi |
| Abstract: | We develop a model of price competition with procrastinating consumers in which market discipline is supposed to arise from both the initial selection of providers and the possibility of switching providers. As in other theories, consumers may forego large gains by sticking with their initially chosen offer, so competition at the switching stage is weak. Unlike in other theories, consumers - who falsely expect to switch soon - may also fail to select the best starting offer, so competition at the initial stage is weak as well. This mechanism can translate temporary product differentiation into permanently high prices, greatly enhance the price effect of persistent differentiation, or generate high markups even with perfect substitutes. Reflecting the same mechanism, sign-up deals do not serve their classically hypothesized role of returning ex-post profits to consumers, but instead often exacerbate the failure of price competition. We complement our analysis with a tailored survey of consumers, confirming the logic of procrastination underlying our model. Consumer procrastination thus emerges as a novel source of competition failure that applies where other theories do not, helping to explain high average prices in many markets with switching costs. |
| Keywords: | procrastination, price competition, competition failure, switching, subscription markets, present bias |
| JEL: | L11 L13 D11 D41 D43 D91 |
| Date: | 2026 |
| URL: | https://d.repec.org/n?u=RePEc:zbw:safewp:340830 |
| By: | Gianluca Grimalda (University of Passau); Fabrice Murtin (OECD Statistics and Data Directorate); David Pipke (Kiel Institute for the World Economy); Louis Putterman (Brown University); Matthias Sutter (Max Planck Institute for Behavioral Economics, Bonn) |
| Abstract: | Pathogen-stress and terror-management theories predict that lethal epidemics heighten parochial cooperation. We test this prediction experimentally in two nationally representative U.S. samples surveyed before and at the onset of the COVID-19 pandemic. We compare trust and expected trustworthiness across the two waves in monetarily incentivized trust games involving non-Hispanic Whites, African Americans, and Hispanics. We find significant ingroup favoritism in both waves. However, the aggregate ingroup premium fell by about one-half between waves. This decline was concentrated among left-leaning and White respondents. Conversely, both African Americans and Hispanics displayed significant ingroup bias in both waves. While non-Hispanic Whites tended to reduce their ingroup bias in expected trustworthiness, the opposite was found for African Americans. Respondents more exposed to COVID-19 displayed higher inter-group trust, altruism and expected trustworthiness than others. These results contradict the hypothesis that lethal epidemics intensify parochialism, also suggesting that the response may be diversified across groups. |
| Keywords: | COVID-19, Pandemic, Inter-group Relationships, Parochialism, Ingroup, Outgroup, Discrimination, Prosociality |
| JEL: | D01 D63 D91 I14 J15 |
| Date: | 2026–04 |
| URL: | https://d.repec.org/n?u=RePEc:mpg:wpaper:2026_04 |
| By: | Ken-Ichi Akao (School of Social Sciences, Waseda University 1-6-1 Nishiwaseda Shinjuku, Tokyo 169-8050, Japan) |
| Abstract: | This paper develops a procedural foundation for the social discount factor. Building on Binmore (2005), we define a procedurally intergenerationally equitable (PIE) path as the outcome of intergenerational bargaining. We then identify the discount factor under which a Ramsey model replicates this path and interpret it as an intergenerationally justifiable (IJ) discount factor. Using tractable models, we show that the IJ discount factor is closely linked to the economic environment. In a benchmark case, the corresponding discount rate coincides with the output elasticity of capital. We further examine a non- overlapping generations model with intergenerational altruism and an overlapping- generations model with individual time preferences, and show how these factors affect the IJ discount factor. These results establish a procedural foundation for the social discount factor and reinterpret discounted utilitarianism within a social contract framework. |
| Keywords: | Intergenerational equity, procedural justice, social discount factor, Ramsey model, bargaining |
| JEL: | D63 D90 C78 Q54 |
| Date: | 2026–05 |
| URL: | https://d.repec.org/n?u=RePEc:was:dpaper:2602 |