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on Game Theory |
| By: | Mehmet Mars Seven |
| Abstract: | We present several models of strategic choice concerning equilibrium reasoning and behaviour, as well as new applications to dynamic games. We propose concepts such as historical equilibrium, simple Nash equilibrium, cautious backward induction, and an approach inspired by how chess players reason in sequential games. |
| Date: | 2026–09 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2609.21163 |
| By: | Juergen Eichberger (Universitat Heidelberg); Simon Grant (Australian National University); David Kelsey (University of Nottingham) |
| Abstract: | We propose Consistent-Planning Equilibrium under Ambiguity (CP-EUA), a solution concept for two-player multi-stage games with almost perfect information. Players evaluate continuation payoffs using a neo-additive representation centred on a behavioural-strategy theory of the opponent. The additive component is identified with the opponent’s behavioural strategy, while the ambiguity component captures the player’s lack of confidence in that theory. The lack-of-confidence parameter is revised by Generalized Bayesian Updating (GBU). Players take account of possible changes in their future ambiguity-sensitive evaluations by using consistent planning. We show that, in the centipede game, ambiguity about the opponent’s strategic behaviour together with sufficient optimism can sustain cooperation for many periods. Similarly, in a non-cooperative bargaining game, ambiguity and optimism may generate delay before agreement is reached. |
| Keywords: | optimism; neo-additive beliefs; extensive-form games; dynamic consistency; consistent planning; centipede game; bargaining |
| Date: | 2026–07 |
| URL: | https://d.repec.org/n?u=RePEc:not:notcdx:2026-07 |
| By: | Martin Bichler; Abheek Ghosh |
| Abstract: | We study equilibrium computation in discrete multiplayer Colonel Blotto games with player-specific battlefield values. In the two-player model with common battlefield values, equilibria can be computed in polynomial time. We show that this tractability breaks down in the multiplayer model with player-specific values under the standard uniform tie-breaking rule. In particular, computing a $(c/n)$-approximate Nash equilibrium is PPAD-hard for some constant $c>0$, even when every player has three resources, where $n$ is the number of players. The main technical step is PPAD-hardness for computing a constant-approximate well-supported Nash equilibrium. In contrast, under uniform tie-breaking, a pure Nash equilibrium can be computed in polynomial time when every player has one resource. We also prove PPAD membership for computing $\varepsilon$-approximate Nash equilibria for inverse-exponentially small $\varepsilon$. Finally, for non-uniform monotone tie-breaking, we show PPAD-hardness even when every player has one resource and all players have identical battlefield values. |
| Date: | 2026–09 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2609.30019 |
| By: | Shani Cohen; Shengwu Li |
| Abstract: | Cursed players understand the distribution of opponents' actions and the distribution of the payoff-relevant state, conditional on their own information, but respond as if the two were independent. Cursed equilibrium additionally requires statistically correct beliefs about the distribution of play. We propose a solution concept that separates the bias from equilibrium: cursed rationalizability iteratively deletes every action that is not a cursed response to a conjecture about opponents' surviving play. The cursed-rationalizable set is the interim correlated rationalizable set of a virtual game, in which payoffs are averaged over the state. Under strategic complements, cursed rationalizability yields the same bounds on behavior as cursed equilibrium. A cautious refinement, the analog of admissibility, delivers sharp predictions in the laboratory games that documented the winner's curse. |
| Date: | 2026–09 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2609.28392 |
| By: | Wolfgang Kuhle |
| Abstract: | We study coordination games in which every action requires planning and preparation. Before players act, they can revise their plans based on partially revealing information about their adversary's preparations. Precise information enables agents to screen for cooperation, selecting the payoff-dominant equilibrium either via small exogenous trembles or via payoff uncertainty. Across scenarios, we emphasize that decomposing an action into (i) preparation and (ii) execution allows us to analyze simultaneous-move games where players partially observe each other's contemporaneous actions. |
| Date: | 2026–09 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2609.17608 |
| By: | David Lagziel; Ehud Lehrer; Tao Wang |
| Abstract: | We analyze incomplete-information games where an oracle publicly shares information with players. One oracle dominates another if, in every game, it can match the set of equilibrium outcomes induced by the latter. Characterizations are provided for deterministic signaling functions, based on simultaneous posterior matching, a constructive partition criterion, and common knowledge components. This study elaborates on the work of Blackwell (1951) in games with incomplete information, using the common knowledge components of Aumann (1976). |
| Date: | 2026–09 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2609.18701 |
| By: | Rod Falvey (Bond University); Tom Lane (Newcastle University); Shravan Luckraz (University of Nottingham Ningbo China); Shuo Yang (University of Nottingham Ningbo China); Wanjun Zheng (Zhejiang University of Finance and Economics) |
| Abstract: | This paper reexamines the Holmström’s moral hazard in teams for environments where team production problems are repeated a finite number of times. Motivated by the observation that many real-world team interactions are naturally repeated while much of the literature emphasizes static peer-evaluation rules or repeated-game constructions that rely on infinite horizons, we adapt a Galbraith Mechanism (GM)-style allocation mechanism to a finitely repeated principal–agent team production setting and evaluate its performance both analytically and in the laboratory. We construct a repeated GM allocation that mixes equal sharing with proportional rewards, characterize subgame-perfect equilibria that sustain higher aggregate effort than static equal-share benchmarks, and design credible finite-horizon history-dependent punishments to select efficient equilibria when multiplicity arises. A laboratory experiment on a twice-repeated game tests the mechanism’s static and dynamic predictions under alternative allocation treatments. Our results show that groups under the (repeated GM) proportional allocation exert significantly higher effort than under (one-shot GM) equal sharing, consistent with theoretical predictions. Observed behavior indicates increased cooperation with repeated interaction. |
| Keywords: | Team Production; Moral Hazard; Finitely Repeated Games; Galbraith Mechanism |
| Date: | 2026–05 |
| URL: | https://d.repec.org/n?u=RePEc:not:notcdx:2026-05 |
| By: | Benjamin Brooks (Department of Economics, University of Chicago); Songzi Du (Department of Economics, University of California—San Diego) |
| Abstract: | We extend the frameworks of Harsanyi (1967) and Mertens and Zamir (1985) to study the higher-order beliefs that groups of individuals obtain by pooling their information. A universal group type space is constructed, which contains all of the belief hierarchies that could be held by any group of players in any type space. This formalism is used to study group belief invariant Bayes correlated equilibria; this is shown to be the minimal solution concept that only depends on group belief hierarchies and contains all Bayes Nash equilibria. |
| Keywords: | Bayes correlated equilibrium, belief invariance, information design, robust predictions. |
| JEL: | C72 D82 D83 |
| Date: | 2026–09–24 |
| URL: | https://d.repec.org/n?u=RePEc:bfi:wpaper:2026-127 |
| By: | Kazimierz Sta\'nczak; Pawel Struski |
| Abstract: | We formulate a complete-information two-player strategic timing game that we refer to as the reverse war of attrition (RWoA). Waiting yields a strictly positive current rent, and the player that outwaits its rival may earn an even higher flow. However, remaining in the waiting state when the rival has moved triggers a discrete late-mover penalty. The distinctive primitive is a player-owned productive buffer which enables the rent-generating activity while waiting, but is degraded by this activity. A rival's move can raise the waiting rent and accelerate depletion. We characterize a unique symmetric equilibrium. We apply RWoA to Bertrand competition in a homogeneous-good market, where vintage inventory serves as the buffer clock for timing repricing. We also discuss competitive maintenance. As an extension, we replicate the bilateral game across a continuum of disjoint heterogeneous local markets and, via the exact law of large numbers, derive deterministic aggregate state shares. |
| Date: | 2026–09 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2609.28178 |
| By: | Benjamin Brooks (Department of Economics, University of Chicago); Songzi Du (Department of Economics, University of California San Diego) |
| Abstract: | A mechanism is participation secure if each agent has an action that guarantees them a payoff better than their outside option, no matter how other agents behave and no matter how uncertainty about preferences is resolved. Participation security implies that every agent’s interim payoff exceeds their outside option, in every information structure and equilibrium. The converse is true if the mechanism is elementary: Every action is the unique best response for some type in some information structure and equilibrium. Elementary mechanisms are shown to be a sufficient class for maximizing the welfare guarantee. Hence, for maximizing the guarantee, participation security is equivalent to interim participation in all information structures and equilibria. |
| Keywords: | Mechanism design, information design, dual reduction, max-min, Bayes correlated equilibrium, robustness, participation security, individual rationality. |
| JEL: | C72 D44 D82 D83 |
| Date: | 2026–09–14 |
| URL: | https://d.repec.org/n?u=RePEc:bfi:wpaper:2026-126 |
| By: | Ian Ball; Drew Fudenberg; Stephen Morris |
| Abstract: | Bayesian monotonicity is a necessary condition for full implementation in Bayes-Nash equilibrium. Under the sequential equilibrium refinement, however, multi-stage mechanisms can expand the scope for implementation. We show that this additional implementation power is fragile. Whenever a multi-stage mechanism sequentially implements a social choice correspondence that is not Bayesian monotone, we construct arbitrarily small "information perturbations'' and show that there are sequential equilibria under these perturbations that yield inadmissible decisions with probability bounded away from zero. Under these perturbations, players' types are not independent conditional on the state and some player is sometimes uncertain of their payoff type. We show by example that the general result fails if perturbations are required to satisfy conditional independence or "known payoff types.'' |
| Date: | 2026–09 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2609.30464 |
| By: | Drew Fudenberg; Andrew Koh |
| Abstract: | We study a continuous-time game in which two firms choose how quickly to advance their capabilities while an exogenous safety threshold advances at a fixed rate. When the capability frontier (max of firms' capabilities) exceeds the safety threshold, all firms are exposed to common disaster that arrives at a hazard rate increasing in the capability-safety difference. We characterize Markov perfect equilibria in terms of the disaster risk, how quickly safety advances, and flow payoffs: when they are low, only racing is an equilibrium; when they are intermediate, racing and pacing coexist; when they are high, only pacing survives. Across all subgame perfect equilibria, low risk induces perpetual racing while high risk rules it out and we bound the probability of disaster across all SPE. If internal capabilities are hidden with a fixed lag until deployment, it is harder to sustain pacing which highlights the importance of transparency about internal capabilities. |
| Date: | 2026–09 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2609.28291 |
| By: | Christos Spyridon Koulouris; Carlo Campajola |
| Abstract: | In this paper, we extend earlier findings of supra-competitive outcomes in optimal-execution games by identifying a learned punitive mechanism that deters deviations and provides behavioural evidence of collusion. We investigate this mechanism in a two-player, finite-horizon Almgren-Chriss liquidation game. Independent proximal policy optimisation agents with access to within-episode price and action histories achieve costs below the Nash benchmark. We identify a profitable deviation by training against the mean learned liquidation schedule, then impose its first trade on one of the original agents. The opponent responds by accelerating liquidation. This response more than offsets the deviator's gain in every run and both player roles, while leaving the punisher's average payoff materially unchanged relative to not punishing under the same deviation. The punisher imposes greater losses on the deviator while preserving its own average payoff, despite the availability of more profitable, less punitive liquidation plans. Matching deviations and subsequent additional selling rise and later decline during training, while final policies retain an effective punitive response. We formalise two checks: whether punishment outweighs the gain from deviating, and whether the change in trading behaviour is large enough to account for the loss imposed. Both checks hold for the tested deviation. Together, these findings provide behavioural and economic evidence supporting a collusive interpretation of the learned supra-competitive outcomes. |
| Date: | 2026–09 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2610.00619 |
| By: | Ziran Liu |
| Abstract: | Bernheim, Braghieri, Mart\'inez-Marquina, and Zuckerman (2021, American Economic Review) develop a theory of chosen preferences and conjecture convergence to pure worldviews at low mindset flexibility. We show that the (original) conjecture fails: with arbitrarily many worldviews, a common-value action sustains mixed worldviews in every stationary equilibrium from a relatively open set of initial worldviews, even when all pure worldviews are absorbing. However, finite linear programs characterize a sufficient persistence condition. Conversely, mixed accumulation points require shared valuation maxima. If each implementable action has a unique maximizing evaluator, every existing stationary equilibrium converges to purity for all interior flexibility and discount parameters. Experienced utility converges without uniqueness. In existing equilibria, small payoff perturbations preserve compromise over fixed horizons with high probability. Strictly tailored worldviews yield existence and a one-step equilibrium characterization at sufficiently low mindset flexibility; weak implementation can preclude stationary pure-strategy existence. The persistence and convergence results extend to stationary randomization. |
| Date: | 2026–09 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2609.19316 |
| By: | Constantine Sorokin; Eyal Winter |
| Abstract: | We study a war of attrition in which each party chooses how far to escalate before conceding. If neither concedes before escalation reaches a random disaster threshold, both receive nothing; otherwise the confrontation ends peacefully. When the parties are ex-ante symmetric and their benefits are independent, improving both parties' private information about their own stakes raises both the probability of peace and each party's ex-ante equilibrium utility. The result holds for every nontrivial mean-preserving spread of posterior values---each party's expected benefit from prevailing given its private information. Higher stakes work in the opposite direction: a first-order stochastic increase in posterior values induces greater persistence, lowers the probability of peace, and can reduce both parties' ex-ante utilities. Starting from symmetry, a sufficiently small improvement in only one party's information also promotes peace; its first-order effect is exactly half that of improving both parties' information. At an asymmetric starting point, however, even a small one-sided improvement can instead lower the probability of peace. |
| Date: | 2026–09 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2609.12210 |
| By: | Fabrizio Adriani (University of Leicester); Abigail Barr (University of Nottingham); Anna Hochleitner (Norwegian School of Economics); Silvia Sonderegger (University of Nottingham) |
| Abstract: | We investigate the impact of rising inequality on social instability through a novel multi-period laboratory experiment. In each period, members of two groups are randomly matched to play a battle of the sexes game, in which payoffs are either zero for both or positive but unequal. At the beginning of the game, the implied payoff inequality is low but, under some treatments, it increases over time. While under low initial inequality, unequal conventions – where one group is systematically better off – tend to emerge, increasing inequality causes destabilization. This is initiated by the group disadvantaged by the unequal convention and is particularly pronounced when not only the relative, but also the absolute position of the disadvantaged group is worsening. These findings are consistent with a simple model incorporating disadvantageous inequality aversion. Finally, we show that history matters; responses to current inequality depend on past experiences of inequality and stability. |
| Keywords: | Inequality; Conflict and Revolutions; Coordination; Group Behavior; Experiments |
| Date: | 2026–04 |
| URL: | https://d.repec.org/n?u=RePEc:not:notcdx:2026-04 |
| By: | Georgy Lukyanov; Yaroslav Yosifov |
| Abstract: | Global games select a unique cutoff when a player's incentive moves monotonically with private information. We show that this logic can fail when a privately informed participant can take a costly, simultaneous, and unobserved action that defends the status quo. In a currency-attack model, the defender acts only at intermediate signals. Along the traders' cutoff equation, this interval response creates an endogenous defense-loss term that vanishes at the endpoints of an activation component but can dominate the decreasing benchmark payoff margin in between. We establish a primitive region in which defense is inactive and uniqueness survives, and a finite-CDF overshoot condition under which two active-defense cutoff roots coexist with the inactive benchmark root. Because marginal indifference need not imply global incentives, we also give sufficient conditions for a genuine monotone cutoff best response. Finally, outward-rounded interval arithmetic proves that a proper-prior parameter vector has exactly three symmetric monotone-cutoff equilibria and that this topology persists locally. The result isolates a payoff-based boundary of global-game selection: hidden intervention can restore multiplicity without public signalling or a perturbation of the information hierarchy. |
| Date: | 2026–09 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2610.00323 |
| By: | Lata Gangadharan (Monash University); Jona Krutaj (University of Nottingham); Maria Claire Villeval (University of Lyon) |
| Abstract: | Heterogeneous returns from contributions to a public good create a normative conflict between equality and efficiency. In a laboratory experiment, we proposed an indicative menu of contribution principles including one featuring a decentralized redistribution mechanism ensuring earnings equality in exchange for fully efficient contributions. Although a majority of individuals, when in the position of an impartial observer, considered this principle to be the most appropriate and expected others to agree, they failed to act on it. Designating a leader who endorsed this principle and made non-binding recommendations enabled a majority of groups to adopt it successfully. This resulted in full contributions and earnings equalization through redistribution from advantaged to disadvantaged members, effectively resolving the conflict. |
| Keywords: | Normative conflict; Redistribution; Efficiency; Leadership; Reciprocity; Experiment |
| Date: | 2026–03 |
| URL: | https://d.repec.org/n?u=RePEc:not:notcdx:2026-03 |
| By: | Yijia Ding |
| Abstract: | This paper provides an explicit characterization of the (unique) equilibrium of the two-bidder all-pay auction with asymmetrically distributed, independent private values. The characterization is achieved through recasting the problem into its equivalence in the quantile space and thereby obtaining equilibrium bid functions that involve only integrals and inverses of the primitives. No regularity assumption is required: the value distributions can be continuous, discrete, singular continuous, or any mixture of these. The explicit formula makes comparative statics transparent. Raising one bidder's value distribution in first-order stochastic dominance raises that bidder's equilibrium bid distribution in the same order. Perturbing a symmetric-bidder model has different revenue effects depending on the direction of the perturbation: whereas slightly weakening one of the two bidders reduces expected revenue, slightly strengthening one of the two has an ambiguous effect. The explicit formula also turns some involved arguments in the literature into direct corollaries. |
| Date: | 2026–09 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2609.14041 |