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on Game Theory |
| By: | Tom Johnston; Michael Savery; Alex Scott; Bassel Tarbush |
| Abstract: | We study the typical structure of games in terms of their connectivity properties. A game is said to be `connected' if it has a pure Nash equilibrium and the property that there is a best-response path from every action profile which is not a pure Nash equilibrium to every pure Nash equilibrium, and it is generic if it has no indifferences. In previous work we showed that, among all $n$-player $k$-action generic games that admit a pure Nash equilibrium, the fraction that are connected tends to $1$ as $n$ gets sufficiently large relative to $k$. The present paper considers the large-$k$ regime, which behaves differently: we show that the connected fraction tends to $1-\zeta_n$ as $k$ gets large, where $\zeta_n>0$. In other words, a constant fraction of many-action games are not connected. However, $\zeta_n$ is small and tends to $0$ rapidly with $n$, so as $n$ increases all but a vanishingly small fraction of many-player-many-action games are connected. Since connectedness is conducive to equilibrium convergence we obtain, by implication, that there is a simple adaptive dynamic that is guaranteed to lead to a pure Nash equilibrium in all but a vanishingly small fraction of generic games that have one. Our results are based on new probabilistic and combinatorial arguments which allow us to address the large-$k$ regime that the approach used in our previous work could not tackle. We thus complement our previous work to provide a more complete picture of game connectivity across different regimes. |
| Date: | 2026–01 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2601.05965 |
| By: | Dylan Possama\"i; Chiara Rossato |
| Abstract: | We investigate a time-inconsistent, non-Markovian finite-player game in continuous time, where each player's objective functional depends non-linearly on the expected value of the state process. As a result, the classical Bellman optimality principle no longer applies. To address this, we adopt a two-layer game-theoretic framework and seek sub-game--perfect Nash equilibria both at the intra-personal level, which accounts for time inconsistency, and at the inter-personal level, which captures strategic interactions among players. We first characterise sub-game--perfect Nash equilibria and the corresponding value processes of all players through a system of coupled backward stochastic differential equations. We then analyse the mean-field counterpart and its sub-game--perfect mean-field equilibria, described by a system of McKean-Vlasov backward stochastic differential equations. Building on this representation, we finally prove the convergence of sub-game--perfect Nash equilibria and their corresponding value processes in the $N$-player game to their mean-field counterparts. |
| Date: | 2025–12 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2512.08745 |
| By: | Suman Chakraborty; Vikash Kumar Dubey; Vaibhav Madhok; Sagar Chakraborty |
| Abstract: | The idea of evolutionarily stable state (ESS) of a population is a cornerstone of evolutionary game theory; moreover, it coincides with the game-theoretic concept of Nash equilibrium. Such a state corresponds to a strategy adopted by the population such that a rare mutant strategy cannot invade the population. In parallel, the dynamical formulation of evolutionary game theory -- particularly through replicator dynamics embodying the tenet of survival of the fittest -- provides a framework for modelling frequency-dependent selection over time. While it is well known that an ESS corresponds to stable fixed point in replicator dynamics, the evolutionary game-theoretic characterization of limit cycles is unknown. Here we fill this lacuna by defining oscillatory ESS (OESS) which we prove to be a stable limit cycle. We also show when an OESS is unique and if there are multiple OESSes, then what their locations are in the phase space. |
| Date: | 2026–01 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2601.01996 |
| By: | Halkos, George; Papageorgiou, George |
| Abstract: | This paper develops a dynamic Stackelberg game between a social planner and a resource-extracting firm to analyze the regulation of renewable resource extraction. The planner, as leader, sets extraction quotas, while the firm, as follower, chooses its extraction effort in response. The model is analyzed under exponential resource growth and compares open-loop (pre-committed) and feedback (state-dependent) equilibrium strategies. We show that open-loop equilibria yield environmentally unstable steady states. Stability can be achieved only under feedback strategies, and only when the follower’s valuation of the resource stock is sufficiently sensitive - a condition met under a quadratic value function. A state-dependent tax is further shown to enhance stability by strengthening the corrective feedback between ecological conditions and extraction incentives. The results highlight the limits of static regulation, underscore the critical role of adaptive, feedback-based policies, and provide a formal argument for precautionary and responsive governance in achieving long-run resource sustainability. |
| Keywords: | Differential games; environmental degradation; exponential growth; logistic growth; sustainable growth; Stackelberg game. |
| JEL: | C61 C62 C72 H23 H32 H62 Q50 Q52 Q53 Q56 |
| Date: | 2026–01–15 |
| URL: | https://d.repec.org/n?u=RePEc:pra:mprapa:127745 |
| By: | Peruchin Tomas Francisco |
| Abstract: | This thesis examines the design of petroleum exploration and production (E&P) rights auctions in Argentina, emphasizing the theoretical and policy implications of President Milei’s 2024 Ley Bases reform to Hydrocarbon Law 17, 319, which introduced royalty bidding as an alternative to the prevailing investment-commitment framework. The study develops a Bayesian auction model in which firms, facing incomplete information, compete after receiving noisy private signals regarding the tract’s underlying value. Two mechanisms are examined: (i) work- commitment bidding, where competition is based on the scale of exploration and production expenditures under a flat royalty; and (ii) royalty bidding, where firms bid a royalty rate rather than committing to a fixed investment level. The symmetric Bayesian Nash equilibrium is characterized by numerically solving coupled integro-differential equations, calibrated to the specific conditions of Argentina’s hydrocarbon sector. The analysis reveals a key policy trade-off: royalty bidding enhances government rent capture but exposes the state to greater fiscal volatility, whereas work-commitment schemes provide more stable, though typically smaller, revenue flows, limiting the upside from high-quality tracts. |
| JEL: | D44 Q35 |
| Date: | 2025–12 |
| URL: | https://d.repec.org/n?u=RePEc:aep:anales:4827 |
| By: | Yifan Dai; Drew Fudenberg; Harry Pei |
| Abstract: | A sender first publicly commits to an experiment and then can privately run additional experiments and selectively disclose their outcomes to a receiver. The sender has private information about the maximal number of additional experiments they can perform (i.e., their type). We show that the sender cannot attain their commitment payoff in any equilibrium if (i) the receiver is sufficiently uncertain about their type and (ii) the sender could benefit from selective disclosure after conducting their full-commitment optimal experiment. Otherwise, there can be equilibria where the sender obtains their commitment payoff. |
| Date: | 2026–01 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2601.05914 |
| By: | Christophe Dutang (LJK - Laboratoire Jean Kuntzmann - Inria - Institut National de Recherche en Informatique et en Automatique - CNRS - Centre National de la Recherche Scientifique - UGA - Université Grenoble Alpes - Grenoble INP - Institut polytechnique de Grenoble - Grenoble Institute of Technology - UGA - Université Grenoble Alpes, ASAR - Applied Statistics And Reliability - ASAR - LJK - Laboratoire Jean Kuntzmann - Inria - Institut National de Recherche en Informatique et en Automatique - CNRS - Centre National de la Recherche Scientifique - UGA - Université Grenoble Alpes - Grenoble INP - Institut polytechnique de Grenoble - Grenoble Institute of Technology - UGA - Université Grenoble Alpes); Clémentine Prieur (AIRSEA - Mathematics and computing applied to oceanic and atmospheric flows - Centre Inria de l'Université Grenoble Alpes - Inria - Institut National de Recherche en Informatique et en Automatique - UGA - Université Grenoble Alpes - LJK - Laboratoire Jean Kuntzmann - Inria - Institut National de Recherche en Informatique et en Automatique - CNRS - Centre National de la Recherche Scientifique - UGA - Université Grenoble Alpes - Grenoble INP - Institut polytechnique de Grenoble - Grenoble Institute of Technology - UGA - Université Grenoble Alpes - Grenoble INP - Institut polytechnique de Grenoble - Grenoble Institute of Technology - UGA - Université Grenoble Alpes) |
| Abstract: | Prioritizing environmental sustainability is a key strategy for securing the health and prosperity of modern societies. In this paper, we study an environmental management problem known as the River Basin Pollution game, where multiple economic agents located along a river may contribute to pollution. An administrative authority seeks to enforce common environmental constraints on those competing industrial agents. To answer this problem, the RBP game is a static noncooperative game, which allows to derive a Pigouvian tax scheme for the agents in practice. We propose a global sensitivity analysis of the proposed game across different types of equilibrium. In contrast to traditional comparative statics analysis, Sobol' indices quantify the contribution of input parameters to the variability of resulting equilibria. |
| Keywords: | non-cooperative game, global sensivitity analysis, Sobol indices parameters, river basin pollution game |
| Date: | 2026–01–16 |
| URL: | https://d.repec.org/n?u=RePEc:hal:journl:hal-05461442 |
| By: | Wei-Chen Lee; Martin Bullinger; Alessandro Abate; Michael Wooldridge |
| Abstract: | We consider a scheduling problem of strategic agents representing jobs of different weights. Each agent has to decide on one of a finite set of identical machines to get their job processed. In contrast to the common and exclusive focus on makespan minimization, we want the outcome to be fair under strategic considerations of the agents. Two natural properties are credibility, which ensures that the assignment is a Nash equilibrium and equality, requiring that agents with equal-weight jobs are assigned to machines of equal load. We combine these two with a hierarchy of fairness properties based on envy-freeness together with several relaxations based on the idea that envy seems more justified towards agents with a higher weight. We present a complete complexity landscape for satisfiability and decision versions of these properties, alone or in combination, and study them as structural constraints under makespan optimization. For our positive results, we develop a unified algorithmic approach, where we achieve different properties by fine-tuning key subroutines. |
| Date: | 2025–12 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2512.13244 |
| By: | Masaaki Fujii (Faculty of Economics, the University of Tokyo) |
| Abstract: | Financial firms and institutional investors are routinely evaluated based on their performance relative to their peers. These relative performance concerns significantly influence risk-taking behavior and market dynamics. While the literature studying Nash equilibrium under such relative performance competitions is extensive, its effect on asset price formation remains largely unexplored. This paper investigates mean-field equilibrium price formation of a single risky stock in a discrete-time market where agents exhibit exponential utility and relative performance concerns. Unlike existing literature that typically treats asset prices as exogenous, we impose a market-clearing condition to determine the price dynamics endogenously within a relative performance equilibrium. Using a binomial tree framework, we establish the existence and uniqueness of the market-clearing mean-field equilibrium in both single- and multi-population settings. Finally, we provide illustrative numerical examples demonstrating the equilibrium price distributions and agents' optimal position sizes. |
| URL: | https://d.repec.org/n?u=RePEc:tky:fseres:2026cf1265 |
| By: | Michela Chessa (GREDEG - Groupe de Recherche en Droit, Economie et Gestion - UNS - Université Nice Sophia Antipolis (1965 - 2019) - CNRS - Centre National de la Recherche Scientifique - UniCA - Université Côte d'Azur); Nobuyuki Hanaki (Osaka University [Osaka]); Aymeric Lardon (GATE Lyon Saint-Étienne - Groupe d'Analyse et de Théorie Economique Lyon - Saint-Etienne - UL2 - Université Lumière - Lyon 2 - UJM - Université Jean Monnet - Saint-Étienne - EM - EMLyon Business School - CNRS - Centre National de la Recherche Scientifique); Takashi Yamada (Yamaguchi University [Yamaguchi]) |
| Abstract: | While market design advocates for the importance of good design to achieve desirable properties, experiments on coalition formation theory have shown fragility in proposed mechanisms to do so. We experimentally investigate the effectiveness of "structured" mechanisms that implement the Shapley value as an ex ante equilibrium outcome with those of corresponding "semi-structured" bargaining procedures. We find a significantly higher frequency of grand coalition formation and higher efficiency in the semi-structured than in the structured procedures regardless of whether they are demand-based or offer-based. While significant differences in the resulting allocations are observed between the two structured procedures, little difference is observed between the two semi-structured procedures. Finally, the possibility of free-form chat induces an equal division more frequently than occurs without it. Our results suggest that when it comes to bargaining and coalition formation, not having various restrictions imposed by different mechanisms may lead to more desirable outcomes. |
| Keywords: | Shapley value, Nash program, Bargaining procedures |
| Date: | 2025–10–16 |
| URL: | https://d.repec.org/n?u=RePEc:hal:journl:hal-05441314 |
| By: | Hao Yu |
| Abstract: | Click-fraud is commonly seen as a key vulnerability of pro-rata revenue sharing on music streaming platforms, whereas user-centric is largely immune. This paper develops a tractable non-cooperative model in which artists can purchase fraud activity that generates undetectable fake streams up to a technological limit. We show that pro-rata can be fraud-robust: when fraud technology is weak, honesty is a strict dominant strategy, and an efficient fraud-free equilibrium obtains. When fraud technology is strong, a unique fraud equilibrium arises, yet aggregate fake streams remain bounded. Although fraud is inefficient, the resulting redistribution may improve fairness in some cases. To mitigate fraud without abandoning pro-rata, we introduce a parametric weighted rule that interpolates between pro-rata and user-centric, and characterize parameter ranges that restore a fraud-free equilibrium under technology constraint. We also discuss implications of Spotify's modernized royalty system for fraud incentives. |
| Date: | 2026–01 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2601.09573 |
| By: | Navin Kartik; Frances Xu Lee; Wing Suen |
| Abstract: | We study voluntary disclosure with multiple biased senders who may bear costs for disclosing or concealing their private information. Under relevant assumptions, disclosures are strategic substitutes under a disclosure cost but complements under a concealment cost. Additional senders thus impede any sender's disclosure under a disclosure cost but promote it under a concealment cost. In the former case, a decision maker can be harmed by additional senders, even when senders have opposing interests. The effects under both kinds of message costs turn on how a sender, when concealing his information, expects others' messages to systematically sway the decision maker's belief. |
| Date: | 2026–01 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2601.10048 |
| By: | I. Sebastian Buhai |
| Abstract: | Wage dispersion and job-to-job mobility are central features of modern labour markets, yet canonical equilibrium search models with exogenous job-offer ladders struggle to jointly account for these facts and the magnitude of frictional wage inequality. We develop a continuous-time equilibrium search model in which match surplus follows a diffusion process, workers choose on-the-job search and separation, firms post state-contingent wages, and the cross-sectional distribution of match states endogenously determines both outside options and the job ladder. On the theoretical side, we formulate the problem as a stationary mean field game with a one-dimensional surplus state, characterize stationary mean field equilibria, and show that equilibrium separation is governed by a free-boundary rule: matches continue if and only if surplus stays above an endogenous threshold. Under standard regularity and Lasry-Lions monotonicity conditions we prove existence and uniqueness of stationary equilibrium and obtain comparative statics for the separation boundary, wage schedules, and wage dispersion. On the quantitative side, we solve the coupled HJB and Kolmogorov system using monotone finite-difference methods and interpret the discretization as a finite-state mean field game. The model is calibrated to micro evidence on stochastic match productivity, job durations, tenure-dependent separation hazards, wage growth, and job-to-job mobility. The stationary equilibrium delivers a structural decomposition of wage dispersion into stochastic selection along job spells, equilibrium on-the-job search and the induced job ladder, and equilibrium wage policies with feedback through outside options. We use this framework to quantify how firing costs, search subsidies, and changes in match-productivity volatility jointly shape mobility, the job ladder, and the cross-sectional distribution of wages. |
| Date: | 2025–12 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2512.07024 |
| By: | Thierry Mayer; Isabelle Méjean; Mathias Thoenig |
| Abstract: | We develop a model of international trade and geopolitical disputes, embedding a diplomatic game of escalation to conflict within a quantitative model of trade. Bilateral disputes arise exogenously, and rival countries engage in negotiations to avoid war. In equilibrium, negotiations may fail, resulting in conflict. All welfare-relevant geoeconomic factors, such as the realized costs of war, the concessions to prevent it, and the probability of escalation, depend on the opportunity cost of war, itself shaped by observed trade flows. We provide a simple procedure to estimate these factors in a model of trade calibrated to current data. This approach is then used to quantify the geoeconomic factors characterizing the US-China relationship, both historically and under various ``decoupling'' scenarios. We find that the growing US dependence to Chinese products and markets over the past thirty years has increased the cost of geopolitical disputes with China for the US. In this context, decoupling from China through increased tariffs may offer geopolitical benefits. Yet, the analysis highlights a fundamental security dilemma: because export and import dependencies influence bargaining power in negotiations, decoupling may reduce the diplomatic concessions needed to maintain peace but can paradoxically raise the risk of escalation by weakening incentives for restraint. |
| Keywords: | International Trade;Geopolitical Disputes;Interstate Conflict;Geoeconomics;Fragmentation;Derisking |
| JEL: | F1 F5 |
| Date: | 2025–12 |
| URL: | https://d.repec.org/n?u=RePEc:cii:cepidt:2025-23 |
| By: | Srinivas Tunuguntla; Carl F. Mela; Jason Pratt |
| Abstract: | Digital advertising platforms and publishers sell ad inventory that conveys targeting information, such as demographic, contextual, or behavioral audience segments, to advertisers. While revealing this information improves ad relevance, it can reduce competition and lower auction revenues. To resolve this trade-off, this paper develops a general auction mechanism -- the Information-Bundling Position Auction (IBPA) mechanism -- that leverages the targeting information to maximize publisher revenue across both search and display advertising environments. The proposed mechanism treats the ad inventory type as the publisher's private information and allocates impressions by comparing advertisers' marginal revenues. We show that IBPA resolves the trade-off between targeting precision and market thickness: publisher revenue is increasing in information granularity and decreasing in disclosure granularity. Moreover, IBPA dominates the generalized second-price (GSP) auction for any distribution of advertiser valuations and under any information or disclosure regime. We also characterize computationally efficient approximations that preserve these guarantees. Using auction-level data from a large retail media platform, we estimate advertiser valuation distributions and simulate counterfactual outcomes. Relative to GSP, IBPA increases publisher revenue by 68%, allocation rate by 19pp, advertiser welfare by 29%, and total welfare by 54%. |
| Date: | 2026–01 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2601.09541 |
| By: | Flandoli, Franco; Leocata, Marta; Livieri, Giulia; Morlacchi, Silvia; Corvino, Fausto; Pirni, Alberto |
| Abstract: | This paper develops two mathematical models to understand subjects’ behavior in response to the urgency of a change and inputs from governments e.g., (subsides) in the context of the diffusion of the solar photovoltaic in Italy. The first model is a Markov model of interacting particle systems. The second one, instead, is a MeanField Game model. In both cases, we derive the scaling limit deterministic dynamics, and we compare the latter to the Italian solar photovoltaic data. We identify periods where the first model describes the behavior of domestic data well and a period where the second model captures a particular feature of data corresponding to companies. The comprehensive analysis, integrated with a philosophical inquiry focusing on the conceptual vocabulary and correlative implications, leads to the formulation of hypotheses about the efficacy of different forms of governmental subsidies. |
| Keywords: | green energy transition; individual based modeling; Markov model; mean-field games; procrastination; solar photovoltaic |
| JEL: | C1 |
| Date: | 2025–07–29 |
| URL: | https://d.repec.org/n?u=RePEc:ehl:lserod:129077 |
| By: | Rouault, Cyril; Zoroglu, Resul |
| Abstract: | This paper examines rebate rules in the context of public goods provision. These rules aim to redistribute the surplus when total contributions exceed the cost of the project. Using an axiomatic approach, we establish impossibility results that highlight the inherent tensions between fairness, participation incentives, and contribution incentives. We then propose and characterize the Proportional Rebate with Threshold rule, which identifies a coherent trade-off across these objectives. |
| Keywords: | Public goods provision, Crowdfunding, Axioms, Rebates, Fairness |
| JEL: | D63 D71 D82 G32 |
| Date: | 2025 |
| URL: | https://d.repec.org/n?u=RePEc:zbw:kitwps:335020 |
| By: | David K Levine |
| Date: | 2026–01–17 |
| URL: | https://d.repec.org/n?u=RePEc:cla:levarc:735347000000000031 |
| By: | David Tan |
| Abstract: | Standard real options theory predicts delay in exercising the option to invest or deploy when extreme asset volatility or technological uncertainty are present. However, in the current race to develop artificial general intelligence (AGI), sovereign actors are exhibiting behaviors contrary to theoretical predictions: the US and China are accelerating AI investment despite acknowledging the potential for catastrophic failure from AGI misalignment. We resolve this puzzle by formalizing the AGI race as a continuous-time preemption game with endogenous existential risk. In our model, the cost of failure is no longer bounded only by the sunk cost of investment (I), but rather a systemic ruin parameter (D) that is correlated with development velocity and shared globally. As the disutility of catastrophe is embedded in both players' payoffs, the risk term mathematically cancels out of the equilibrium indifference condition. This creates a "suicide region" in the investment space where competitive pressures force rational agents to deploy AGI systems early, despite a negative risk-adjusted net present value. Furthermore, we show that "warning shots" (sub-existential disasters) will fail to deter AGI acceleration, as the winner-takes-all nature of the race remains intact. The race can only be halted if the cost of ruin is internalized, making safety research a prerequisite for economic viability. We derive the critical private liability threshold required to restore the option value of waiting and propose mechanism design interventions that can better ensure safe AGI research and socially responsible deployment. |
| Date: | 2025–12 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2512.07526 |
| By: | Antonio Cabrales; Esther Hauk |
| Abstract: | This paper develops a model to understand the conditions under which groups within a society choose between a collaborative and an individualist approach to education. A key feature of the model is the presence of externalities, which can lead to multiple equilibria. This framework helps explain the persistence of diverse local educational cultures, even within relatively homogeneous countries. These features yield important and subtle insights for public policy. Policymakers may need to focus either on shifting beliefs or enhancing the abilities of parents and teachers. We also analyze the incentives driving segregation in education and explore potential policy responses. |
| Keywords: | collaborative learning, Coordination, education policy, Externalities, local interaction, multiple equilibria, parental educational styles, peer effects, school choice, segregation |
| JEL: | I21 D62 C72 I28 |
| Date: | 2026–01 |
| URL: | https://d.repec.org/n?u=RePEc:bge:wpaper:1546 |
| By: | Romain Biard (Université Marie et Louis Pasteur, LmB, UMR6623, F-25000 Besançon, France); Mostapha Diss (Université Marie et Louis Pasteur, CRESE UR3190, F-25000 Besançon, France); Salma Larabi (Université Marie et Louis Pasteur, CRESE UR3190, F-25000 Besançon, France) |
| Abstract: | We propose a weighted minority voting mechanism within a two-round sequential voting process, in which all individuals retain their voting rights in the second round but with different weights depending on the first-round outcome. In a utilitarian framework where individuals have a given utility function that depends on the outcomes of each round, first-round winners are identified and vote with reduced weight in the second round, while losers retain full weight. By giving greater weight to first-round losers, this design ensures that first-round winners continue to contribute to the final decision without dominating it, thereby mitigating repeated disadvantages for losers. We then compare the expected aggregate utility of society across different levels of second-round weight assigned to first-round losers, including both the simple majority rule – where all voters carry equal weight in both rounds – and the limiting case of minority voting where first-round losers receive no weight in the second round. To do so, we analyze two models: one in which individual utility derives solely from material payoffs, and another in which a form of harmony is considered, whereby individuals incur a utility loss if others repeatedly belong to the losing minority. This analysis allows us to assess how strategic behavior affects the effectiveness of the proposed mechanism. |
| Keywords: | Voting, Minority Voting, Simple Majority, Utilitarianism, Harmony. |
| JEL: | C72 D70 D71 D72 |
| Date: | 2026–01 |
| URL: | https://d.repec.org/n?u=RePEc:crb:wpaper:2026-01 |