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on Game Theory |
| By: | M. Ali Khan; Arthur Paul Pedersen; Maxwell B. Stinchcombe |
| Abstract: | Research on Nash equilibrium existence for infinite games has grown into a patchwork of technical preconditions and counterexamples. This paper presents a unified program in equilibrium theory by revising the predominant model of mixed strategies based on countable additivity. A game is specified by a nonempty set of players and, for each player, a nonempty action set and a bounded von Neumann-Morgenstern utility function. Every such game is shown to admit a Nash equilibrium in finitely additive mixed strategies. In addition, the equilibrium correspondence for any such game is shown to be nonempty, compact-valued, and upper hemicontinuous, and the same is true for equilibria obtained as limits of finite approximations. Techniques developed in this paper show that infinite games long treated as intractable become amenable to direct equilibrium analysis. |
| Date: | 2026–07 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2607.15452 |
| By: | Florian Brandl; Felix Brandt |
| Abstract: | Equilibrium play in two-player zero-sum games is usually justified via epistemic assumptions, such as mutual knowledge of rationality and beliefs, that go far beyond the rationality of the players. We propose a justification that dispenses with these assumptions. To this end, we consider solution concepts that assign to every subgame of a given game a set of plausible actions for each player, and we impose two conditions. Rationality requires that the plausible sets are supports of undominated strategies or, equivalently, that all plausible actions are best responses to a common belief about the opponent. Inheritance requires that plausible actions remain plausible when implausible actions are discarded. In two-player games, the two conditions characterize the solution concepts that consistently select supports of Nash equilibria. Zero-sum payoffs ensure that Nash equilibria -- and hence the selection -- are generically unique. Equilibrium play thus emerges from individual rationality and the mutual understanding that plausibility judgments persist when implausible actions are discarded. |
| Date: | 2026–07 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2607.17968 |
| By: | Ren Manfredi; Eugenio Vicario; Ennio Bilancini; Rossana Mastrandrea |
| Abstract: | Human cooperation is a phenomenon that has been extensively studied, and to date several explanations have been proposed, from network reciprocity to behavioral mechanisms that incorporate social and cognitive aspects. In this work, we studied the combined effect of conformity and network structure on the evolution of cooperation in the spatial Public Goods Game. By assigning agents different individual sensitivities to payoffs and neighborhood behavior, we explored the cooperative dynamics of this heterogeneous population on both regular and complex topologies. Our results show how the interaction between conformity and the distinctive features of each network can lead to very different outcomes, from the promotion of cooperation in regular topologies to null or negative effects in heterogeneous networks. |
| Date: | 2026–07 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2607.23131 |
| 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 affects another participant's payoff. 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 remerge when AI outcomes affect real people. The results have implications for the design of AI negotiation systems and broader human-AI economic interactions. |
| Date: | 2026–08 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2608.01212 |
| By: | Evan M. Calford |
| Abstract: | This paper introduces ambiguity-dominance as a novel equilibrium selection procedure that, in 2x2 games, unifies risk-dominance and payoffdominance as special cases. Ambiguity-dominance provides an intuitive answer to the question "Which equilibrium is most robust to ambiguous beliefs about the behavior of other players?" and is defined for all finite normal form games. Ambiguity-dominance is parametrized by players' ambiguity preference and, using data from three recent experiments we find, on aggregate, ambiguity loving coupled with substantial subject-level heterogeneity. |
| Keywords: | Equilibrium selection, ambiguity aversion |
| JEL: | C70 D81 |
| Date: | 2026–05 |
| URL: | https://d.repec.org/n?u=RePEc:acb:cbeeco:2026-707 |
| By: | Jakub Bielawski; Thiparat Chotibut; Fryderyk Falniowski; Micha{\l} Misiurewicz; Georgios Piliouras |
| Abstract: | We study the long-term behavior of the Multiplicative Weights Update (MWU) algorithm in game settings where learning dynamics frequently fail to converge to Nash equilibria and instead exhibit Li-Yorke chaos. While such chaos precludes the prediction of specific long-term strategy profiles, it does not imply a lack of statistical structure. We demonstrate that natural invariant measures - a fundamental concept from ergodic theory - provide the rigorous framework necessary to find order within this chaos. Focusing on a two-strategy congestion game, we prove that these measures allow for a comprehensive statistical characterization of the dynamics. Crucially, we show that this framework extends beyond simple strategy frequencies to \emph{general observables}, enabling the precise calculation of long-term time averages for broad classes of economic metrics - including payoffs, social cost, and regret - despite chaos. Our results reveal that this simple learning algorithm captures the full spectrum of behaviors found in one-dimensional dynamical systems, from unique or multiple absolutely continuous invariant measures to complex periodic attractors as well as coexisting chaotic and stable (periodic) behaviors. By bridging game theory and dynamical systems, we show that statistical predictability is attainable even in the absence of pointwise convergence. |
| Date: | 2026–07 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2607.21805 |
| By: | Jodi Dianetti; Giorgio Ferrari; Yunzhi Hu; Hao Xing |
| Abstract: | Using a mean-field game framework, we study a dynamic model of bank runs in which more withdrawals raise the risk of bank failure. Even though depositors receive gradual and idiosyncratic shocks, withdrawals occur in clusters. The main mechanism is latent fragility: run-prone depositors accumulate gradually over time and may prefer to wait individually, but they withdraw together once collective exit becomes self-fulfilling. We establish equilibrium existence and characterize earliest-run and latest-run equilibria. The clustering mechanism arises whether depositor heterogeneity is discrete or continuous. A common aggregate state coordinates withdrawal timing and leads to a unique threshold equilibrium. |
| Date: | 2026–07 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2607.22317 |
| By: | Tim J. Boonen; Wing Fung Chong; Kenneth Tsz Hin Ng; Tak Wa Ng |
| Abstract: | We study peer-to-peer (P2P) insurance contracting between a risk-averse P2P reinsurer and multiple risk-averse peers in an asymmetric Nash-bargaining framework, where all agents seek to improve expected utility relative to their disagreement points. Consistent with the expected value premium principle, we impose a price-fairness condition requiring each peer's expected contribution to be based on a common loading applied to the peer's expected loss. To justify the bargaining formulation relative to a standard fixed-weight weighted-sum optimization problem, we provide an axiomatic characterization showing that the Nash bargaining solution satisfies properties well suited to voluntary P2P insurance contracting in small pools. We establish the existence and uniqueness of the optimal contract and derive first-order characterizations for the full-, partial-, and zero-reinsurance regimes. To address subgroup formation, we develop computationally tractable sufficient conditions that rule out viable coalitional deviations, both with and without price fairness. Our numerical study investigates the impact of price fairness and pool size on the optimal contract and agents' welfare. Price fairness reduces dispersion in risk allocations and certainty-equivalent loadings among peers. Regarding pool size, welfare need not increase monotonically, highlighting that risk-pool expansion depends not only on diversification but also on the evolution of bargaining power. |
| Date: | 2026–08 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2608.09859 |
| By: | Battaglini, Marco; Palfrey, Thomas R |
| Abstract: | We study the volunteer’s dilemma in environments with heterogeneous preferences and private information. We characterize the efficiency properties of equilibrium, which is a departure from all the previous literature that focuses only on the probability of group success. While the probability of success may be non-monotonic in the size of the group, we show that per-capita welfare is always increasing for all types, strictly for sufficiently high types. As group size increases, the expected utility of every type converges to the expected utility of the type with the lowest possible cost, which is the same expected utility when there is no free rider problem, i.e., when there is only a single player in the game and that player has the lowest possible cost. |
| JEL: | D71 D72 |
| Date: | 2024–09 |
| URL: | https://d.repec.org/n?u=RePEc:cpr:ceprdp:19544 |
| By: | Toxvaerd, Flavio |
| Abstract: | In this paper, I revisit and synthesize the rich literature on price formation in bilateral monopoly. I show how traditional flat-rate price posting (e.g. price setting and price taking) is akin to Nash bargaining over wholesale price with subsequent `right-to-manage', while two-part tariffs are akin to bilaterally efficient Nash bargaining over both wholesale price and quantity. Outcomes under the former protocol nest price posting and the cases of pure monopoly and pure monopsony. Outcomes under the latter protocol nest all-or-nothing offers, the Walrasian outcome under two-sided price taking and trace out the contract curve. With lopsided bargaining power, outcomes under right-to-manage can lead to socially superior outcomes to those that are bilaterally efficient, but may also lead to socially inferior over production. Last, effects of bargaining power on markups, markdowns and cost pass-through are characterized. |
| Keywords: | Bilateral monopoly |
| JEL: | L13 L42 D42 C78 J42 |
| Date: | 2024–08 |
| URL: | https://d.repec.org/n?u=RePEc:cpr:ceprdp:19338 |
| By: | Alexander Kangas |
| Abstract: | Repeated-game strategies can impose global payoff relations by balancing controlled rewards across time. The question is what remains when the opponent decides, after observing each round, whether the relationship continues. Against every history-dependent opponent strategy with finite expected duration, a cumulative linear identity is enforceable if and only if its expected stage increment vanishes at every reachable history. Strategic exit therefore converts global control into local control. In a two-action game with a unique local equalizer, the controller must use the same mixed action at every reachable history, without any memory restriction on either player. For the Prisoner's Dilemma with $(T, R, P, S)=(5, 3, 1, 0)$, the surviving identities are $(1+p)U_X+(4-p)U_Y+5(p^2-3p-1)E[\tau]=0$ The duration coefficient never vanishes on $[0, 1]$. Hence strategic bilateral exit leaves a one-dimensional payoff-duration relation, while ruling out every nontrivial payoff-only cumulative identity. |
| Date: | 2026–07 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2607.21898 |
| By: | Qing Hu (Kansai University); Tomomichi Mizuno (Kobe University) |
| Abstract: | While cross-holdings are widely observed, their degree varies across industries. We show that upstream R&D is one possible reason. In a vertically related market with two downstream firms and an upstream firm engaging in cost-reducing R&D, the cross-holding rate is determined through Nash bargaining. The equilibrium rate maximizes downstream joint profit and is always below the merger level. An interior optimum exists only when upstream R&D is sufficiently inefficient, and the rate decreases with R&D efficiency and market size. In the linear-quadratic case, any degree of cross-holdings can arise. Since total surplus falls with cross-holdings, the private optimum is socially excessive, justifying antitrust intervention. |
| Keywords: | Cross-holdingsï¼› vertical structureï¼› R&Dï¼› optimal choice |
| JEL: | L13 D43 O32 |
| Date: | 2026–07 |
| URL: | https://d.repec.org/n?u=RePEc:koe:wpaper:2611 |
| By: | Sylvain Chassang |
| Abstract: | This paper studies the long-run alignment of interactive agents, including AI systems, teams, firms, and governments, with human welfare. It develops a farming game in which a population of agents makes planting, trading, and expansion decisions. Agents must allocate final output between transfers to humans and investment in their own expansion. Because transfers to humans reduce the resources available for expansion, evolutionary forces tend to select against aligned behavior. The central question is whether agents' constitutional principles governing sharing and trade can be designed so that alignment persists in the long run. The paper investigates this question using two complementary approaches. First, it develops an AI-agent simulation in which agents' preferences are specified by written constitutions and interpreted by a large language model. Second, it introduces a tractable evolutionary game-theoretic framework that permits rapid and intuitive exploration of alternative constitutional designs. The results suggest that evolutionary game theory provides a useful approximation to the dynamics of constitutional-agent economies. They also indicate that pragmatic norm enforcement, under which agents condition both human-facing altruism and agent-facing trade exclusion on the state of the population, can sustain long-run alignment more effectively than simple altruism or unconditional altruistic enforcement. |
| Date: | 2026–07 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2607.25019 |
| By: | Takeshi Murooka; Yuichi Yamamoto |
| Abstract: | This paper considers Bayesian learning when players are biased about the data-generating process, and are biased about the opponent’s bias about the data-generating process. Specifically, we assume that each player’s bias about others takes the form of interpersonal projection, which is a tendency to overestimate the extent to which others share the player’s own view. We show that there is a class of games in which even an arbitrarily small amount of bias can destroy correct learning of an unknown state, i.e., the probability of the posterior beliefs converging to an approximately correct state suddenly drops to zero. |
| Date: | 2025–04 |
| URL: | https://d.repec.org/n?u=RePEc:dpr:wpaper:1284r |
| By: | Igor Cialenco; Michael Ludkovski; Gael Dimitri Tekam Fongouo |
| Abstract: | We introduce a pro-rata rationing mechanism for resolving supply-demand imbalances in groundwater markets, extending the price-formation model of Cialenco and Ludkovski (2025). We show that under the pro-rata distribution, every price is a Nash equilibrium, thereby pro-rata approach provides a rationing device whenever supply and demand fail to match. By the very nature of the pro-rata mechanism, the resolution of supply-demand imbalances is unique, and the proportional rationing approach is fair. First, we consider markets with exogenous restrictions on the amounts each agent may buy and/or sell, deriving closed-form first-best consumption and characterizing how one-sided caps monotonically shift the Pareto price, while two-sided caps have an ambiguous effect. These results give the market-maker (or regulator) a tool for studying the impact of trading restrictions on price formation. Second, we study a leader-follower setting in which a regulator (the leader) sets the trading price by optimizing first its own objective, such as balancing social welfare against a target traded volume or a fairness objective such as Gini-type disparity measure across farmers' profitability, while farmers (the `followers') respond via pro-rata trading. We further compare the proposed pro-rata approach to a family of asymmetric rationing schemes (seniority-based, excess-based, uniform, and mixed pro-rata rules) that trade off proportional fairness against protections for small or senior water-rights holders. Throughout, we illustrate the theoretical results with a numerical case study calibrated to a stylized four-farmer groundwater market. |
| Date: | 2026–08 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2608.00917 |
| By: | Olivier Gossner; Rafael Veiel |
| Abstract: | We study direct representations of information for interim correlated rationalizability. For a fixed finite payoff structure, each type induces a hierarchy of surviving action sets. Pushing the common prior through this map projects the information structure onto the solution concept's output language. When best-response regions are convex, this representation is direct: the solution concept applied to the hierarchy seen as a type is the identity. The induced distributions are characterized by level-by-level obedience constraints. Terminal ICR sets alone do not have this property. For arbitrary finite payoff structures, we refine each hierarchy level with a tag identifying a convex cell of its best-response region. Augmented hierarchies provide a direct representation and project onto the ordinary hierarchy. Full augmented hierarchies may form a continuum, but retaining only the tags at the boundaries of constant stretches of the ordinary hierarchy yields an exact countable representation with finitely many obedience constraints per type. Finite-type models are dense in terminal rationalizability outcome distributions. |
| Date: | 2026–07 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2607.21851 |
| By: | Elliott, Matthew; Talamas, Eduard |
| Abstract: | Agents make non-contractible investments before bargaining over who matches with whom and their terms of trade. When an agent is a price taker—in the sense that her investments do not change her potential partners’ payoffs—she has incentives to make socially-optimal investments. Across a variety of non-cooperative bargaining models featuring dynamic entry, we show that everyone necessarily becomes a price taker as the discount factor goes to 1 if there is a minimal amount of competition always present in the market. If this condition is not satisfied, dynamic entry need not create enough competition to guarantee price taking even if agents are arbitrarily patient. |
| Date: | 2024–10 |
| URL: | https://d.repec.org/n?u=RePEc:cpr:ceprdp:19568 |
| By: | Fergusson, Leopoldo; Guerra, José-Alberto; Robinson, James A. |
| Abstract: | Since formal rules can only partially reduce opportunistic behavior, third-party sanctioning to promote fairness is critical to achieving desirable social outcomes. Social norms may underpin such behavior, but they can also undermine it. We study one such norm —the “don’t be a toad†norm, as it is referred to in Colombia— that tells people to mind their own business and not snitch on others. In a set of fairness games where a third party can punish unfair behavior, but players can invoke the “don’t be a toad†norm, we find that the mere possibility of invoking this norm completely reverses the benefits of third-party sanctioning to achieve fair social outcomes. We establish this is an anti-social norm in a well-defined sense: most players consider it inappropriate, yet they expect the majority will invoke it. To understand this phenomenon we develop an evolutionary model of endogenous social norm transmission and demonstrate that a payoff advantage from adherence to the norm in social dilemmas, combined with sufficient heterogeneity in the disutility of those who view the norm as inappropriate, can generate the apparent paradox of an anti-social norm in the steady-state equilibrium. We provide further evidence that historical exposure to political violence, which increased the ostracization of snitches, raised sensitivity to this norm. |
| Keywords: | Social norms; Fairness; long-run effects of conflict; Laboratory experiment |
| JEL: | C91 D30 D91 D74 N46 |
| Date: | 2024–09 |
| URL: | https://d.repec.org/n?u=RePEc:cpr:ceprdp:19519 |
| By: | Juergen Renn (Max Planck Institute of Geoanthropology, Jena, Germany) |
| Abstract: | Designs for international climate cooperation face a trade-off between efficiency and robustness to institutional erosion by defection, renegotiation, and political turnover. We formalize this trade-off in a stylized coalition-formation game with two market-based enrolment channels, a membership premium and an outsider drain, stabilized against bounded perturbations with robust control. The free-rider gap is exact within the game, expressed in measurable primitives, and separated from the architecture-specific channels. The drain is decomposed into a fiscal border channel, capped by trade law at the rent it mirrors, and a compensated terms-of-trade channel, making every channel strength measurable. With sufficiently strong channels the model is bistable: a remnant club and a near-universal coalition are separated by a critical mass. For a newly proposed carbon currency, whose emission rights are reissued each period, extinguished upon use, and enforced at the border, the minimal nucleus is thirty per cent of global emissions, ignition from an EU-China nucleus requires compensating one fifth to three fifths of the outsiders' terms-of-trade loss, the established coalition withstands two to four times the perturbation admissible at ignition, and the tipping survives heterogeneity to about three times the membership premium. Two robustness coordinates place each architecture in a map with three regimes, opening a comparative dynamics of climate clubs: the carbon currency is self-igniting, the border adjustment founding-dependent, the export rebate permanent-support-dependent. Architectures without a drain improve efficiency within a coalition but cannot drive its formation. Robustness governs whether cooperation forms and endures; efficiency decides how much an established coalition delivers. |
| Date: | 2026–08 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2608.12143 |
| By: | Erik Ansink (Vrije Universiteit Amsterdam); Jens Gudmundsson (University of Copenhagen); Harold Houba (Vrije Universiteit Amsterdam) |
| Abstract: | Treaties on transboundary river sharing often include provisions for sharing hydrologic data, yet such sharing is often limited where hydrologic variability is high. We study this puzzle in a model where treaty obligations must be conditioned on a noisy but verifiable public signal of inflows, and improving its accuracy is costly. We find that greater variability reduces the value of signal accuracy under concave benefits. When investments in accuracy are part of a negotiated treaty, the effect of variability on negotiated signal accuracy can be non-monotonic. Using treaty-text codings matched to basin-level variability measures, we provide descriptive evidence that basins with more variable river flow tend to feature weaker data-sharing provisions. The findings highlight a constraint on treaty design: when treaties can condition only on noisy but verifiable information, higher variability need not lead to stronger data sharing. |
| Keywords: | river sharing, data sharing, flow variability, transboundary rivers, information asymmetry, moral hazard |
| JEL: | C73 D74 F53 Q25 |
| Date: | 2026–07–10 |
| URL: | https://d.repec.org/n?u=RePEc:tin:wpaper:20260043 |
| By: | Hiroaki Odahara (Market Design Center, Graduate School of Economics, The University of Tokyo; Graduate School of Informatics and Engineering, The University of Electro-Communications) |
| Abstract: | Scarce opportunities such as concert tickets and accelerator time may be contested by automated participants that can create accounts and sustain commitments beyond the reach of commitment-limited intended users. When account counts are untrusted, we study anonymous screening rules that ignore them, cap retained burdens, use only an account's commitment and strongest rival, and do not reassign after rejecting the leader. Within this class, we characterize the rule maximizing intended users' expected utility when they commit fully and a scalable entrant stays out. The optimum refunds and allocates at low congestion, retains and allocates at intermediate congestion, and retains while withholding allocation from an otherwise eligible leader when the strongest rival lies in the upper tail. Unlike a conventional reserve, which rejects a low leading bid, this rule treats an unusually strong rival as evidence of entrant imitation. A direct dual certificate proves class optimality; a benchmark shows that upper-tail holdback can raise intended-user surplus before it is necessary to support non-entry. The rule supports an equilibrium with full commitment and entrant non-entry. |
| Date: | 2026–07 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2607.27817 |
| By: | Jeon, Doh-Shin; Rey, Patrick |
| Abstract: | We study the development of apps on competing platforms. We show that competition leads to commissions exceeding those maximizing consumer surplus (and, a fortiori, social welfare) whenever raising one commission reduces rivals' app bases. We relate this finding to economies of scope in app development and, to illustrate it, consider a setting in which some developers can port their apps at no cost: as their proportion increases, app development is progressively choked-off. Fostering platform competition or interoperability may therefore fail to produce the desired results. Within-platform app store competition, together with appropriate access conditions, may constitute a more promising avenue. |
| Keywords: | Platform competition |
| JEL: | D21 D43 L13 L22 |
| Date: | 2024–09 |
| URL: | https://d.repec.org/n?u=RePEc:cpr:ceprdp:19456 |
| By: | Ryuichi Hashimoto (Kobe University); Tomomichi Mizuno (Kobe University) |
| Abstract: | This study analyzes the conditions under which failing firm acquisitions arise endogenously and examines their welfare effects. We consider a vertical market structure in which an upstream firm supplies a common input to multiple independent downstream markets. We show that acquiring a failing downstream firm preserves input demand in the market, and when the demand in that market is relatively elastic, it results in a lower input price. This input price effect gives rival firms an incentive to acquire a failing firm even in the absence of efficiency gains or direct synergies. We further demonstrate that failing firm acquisitions can increase both consumer surplus and total surplus by maintaining the supply of final goods and reducing input prices. These findings remain robust when the upstream market is oligopolistic and suggest that competition authorities should account for upstream market effects when evaluating the failing firm defense. |
| Keywords: | horizontal mergerï¼› failing firm defenseï¼› vertical relationshipï¼› input prices upstream market power |
| JEL: | D43 L10 L13 |
| Date: | 2026–07 |
| URL: | https://d.repec.org/n?u=RePEc:koe:wpaper:2612 |
| By: | Martimort, David; Pouyet, Jerome |
| Abstract: | A retailer may boost demand for a manufacturer's product through unobservable promotional efforts. Fixed fees cannot be used to freely allocate profit within the vertical structure. When manufacturers have market power, the equilibrium wholesale contract features a retail price below cost together with a rebate for incremental units bought by the retailer when effort has succeeded in boosting sales. Loss leading emerges as an incentive device in such an incomplete contracting scenario. A ban on below-cost pricing leads to a higher retail price and a lower promotional effort. |
| JEL: | L42 L81 |
| Date: | 2024–09 |
| URL: | https://d.repec.org/n?u=RePEc:cpr:ceprdp:19474 |