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on Game Theory |
| By: | Cristian Chica; Yinglong Guo; Gilad Lerman |
| Abstract: | There is growing experimental evidence that $Q$-learning agents may learn to charge supracompetitive prices. We provide the first theoretical explanation for this behavior in infinite repeated games. Firms update their pricing policies based solely on observed profits, without computing equilibrium strategies. We show that when the game admits both a one-stage Nash equilibrium price and a collusive-enabling price, and when the $Q$-function satisfies certain inequalities at the end of experimentation, firms learn to consistently charge supracompetitive prices. We introduce a new class of one-memory subgame perfect equilibria (SPEs) and provide conditions under which learned behavior is supported by naive collusion, grim trigger policies, or increasing strategies. Naive collusion does not constitute an SPE unless the collusive-enabling price is a one-stage Nash equilibrium, whereas grim trigger policies can. |
| Date: | 2025–05 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2505.22909 |
| By: | Yan Liu; Ying Qin; Zihe Wang |
| Abstract: | The all-pay auction, a classic competitive model, is widely applied in scenarios such as political elections, sports competitions, and research and development, where all participants pay their bids regardless of winning or losing. However, in the traditional all-pay auction, players have no budget constraints, whereas in real-world scenarios, players typically face budget constraints. This paper studies the Nash equilibrium of two players with budget constraints across multiple heterogeneous items in a complete-information framework. The main contributions are as follows: (1) a comprehensive characterization of the Nash equilibrium in single-item auctions with asymmetric budgets and valuations; (2) the construction of a joint distribution Nash equilibrium for the two-item scenario; and (3) the construction of a joint distribution Nash equilibrium for the three-item scenario. Unlike the unconstrained all-pay auction, which always has a Nash equilibrium, a Nash equilibrium may not exist when players have budget constraints. Our findings highlight the intricate effects of budget constraints on bidding strategies, providing new perspectives and methodologies for theoretical analysis and practical applications of all-pay auctions. |
| Date: | 2025–05 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2505.03291 |
| By: | Debora Princepe; Onofrio Mazzarisi; Erol Akcay; Simon A. Levin; Matteo Marsili |
| Abstract: | Happiness, in the U.S. Declaration of Independence, was understood quite differently from today's popular notions of personal pleasure. Happiness implies a flourishing life - one of virtue, purpose, and contribution to the common good. This paper studies populations of individuals - that we call homo-felix - who maximise an objective function that we call happiness. The happiness of one individual depends on the payoffs that they receive in games they play with their peers as well as on the happiness of the peers they interact with. Individuals care more or less about others depending on whether that makes them more or less happy. This paper analyses the happiness feedback loops that result from these interactions in simple settings. We find that individuals tend to care more about individuals who are happier than what they would be by being selfish. In simple 2 x 2 game theoretic settings, we show that homo-felix can converge to a variety of equilibria which includes but goes beyond Nash equilibria. In an n-persons public good game we show that the non-cooperative Nash equilibrium is marginally unstable and a single individual who develops prosocial behaviour is able to drive almost the whole population to a cooperative state. |
| Date: | 2025–06 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2506.10537 |
| By: | Samiha Tariq |
| Abstract: | This paper examines the impact of cognitive biases on financial decision-making through a static Bayesian game framework. While traditional economic theory assumes fully rational investors, real-world choices are often shaped by loss aversion, overconfidence, and herd behavior. Integrating psychological insights with economic game theory, the model studies strategic interactions among investors who allocate wealth between risky and risk-free assets. Solving for the Bayesian Nash Equilibrium reveals that each bias distorts optimal portfolios and alters aggregate market dynamics. The results echo Herbert Simon's notion of bounded rationality, showing how biases can generate market inefficiencies, price bubbles, and crashes. The findings highlight the importance of incorporating psychological factors into economic models to guide policies that foster market stability and more informed financial decision-making. |
| Date: | 2025–05 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2505.18835 |
| By: | Georg Kirchsteiger; Tom Lenaerts; Remi Suchon |
| Abstract: | Experimental evidence shows that in a repeated dilemma setting cooperation is more likely to become the norm in small matching groups than in large ones. This result holds even if cooperation is an equilibrium outcome for all investigated group sizes. But what happens if small matching groups are merged to become large ones? Our paper is based on the idea that due to norm spillovers, a large group created by a merger of small groups is more likely to cooperate than a large group of similar size that is created directly. We tested this idea experimentally in the context of an infinitely repeated prisoner’s dilemma game. We compared the cooperation behavior of groups that result from mergers of smaller groups with the cooperation behavior of groups with constant group size. We found that cooperation levels were significantly higher in large groups that resulted from gradual growth than in large groups of the same size that were directly created. Looking at the individual behavior, we see that more subjects develop a norm of unconditional cooperation when the group size increases than when it is already large from the beginning. Hence, our results confirm the idea that cooperation is much more likely to be achieved when groups grow from small to large than when large groups are formed directly. |
| Keywords: | Prisoner’s dilemma, Cooperation in repeated games, Group growth, Norm spillover |
| Date: | 2025–06 |
| URL: | https://d.repec.org/n?u=RePEc:eca:wpaper:2013/391301 |
| By: | Frédéric Deroïan (Aix-Marseille Univ., CNRS, AMSE, Marseille); Mohamed Belhaj (Aix-Marseille Univ., CNRS, AMSE, Marseille) |
| Abstract: | This paper introduces demotivation in the context of social comparison in networks. Social comparison is modeled as a status effect rewarding or penalizing agents according to their relative performance with respect to local peers. A demotivated agent faces both a reduced marginal return to effort and a psychological cost. In the absence of demotivation, social comparison leads to higher effort levels but reduces equilibrium welfare. Introducing demotivation leads to two main findings. First, it generates a network game of strategic substitutes. Second, despite the individual psychological costs incurred by demotivated agents, it can enhance overall welfare—by alleviating social pressure to exert effort and by generating positive externalities for peers. |
| Keywords: | Social Comparison; Demotivation; Networks; Strategic Substitutes, Equilibrium Welfare. |
| JEL: | C72 D83 D85 |
| Date: | 2025–05 |
| URL: | https://d.repec.org/n?u=RePEc:aim:wpaimx:2511 |
| By: | Joshua S. Gans |
| Abstract: | The canonical example of unprotected speech—falsely shouting “fire” in a crowded theatre—presumes such an act inevitably causes harmful panic. This paper challenges that presumption through a game-theoretic analysis of evacuation dynamics. I model a theatre as an N × M grid where rational patrons navigate spatial constraints while evacuating. Strategic conflicts arise only when patrons are equidistant from exits, creating localized “clash games” that admit multiple equilibria, including numerous pure-strategy equilibria that achieve zero-collision evacuations. Using global games methodology, I show that strategic uncertainty uniquely selects an equilibrium, where those entering from rows have precedence over those already in aisles. However, introducing a panic mechanism based on accumulated waiting time reveals a tension: the strategically optimal East-priority equilibrium proves most vulnerable to behavioral breakdown, while the alternating equilibrium exhibits superior robustness to panic. These findings suggest that whether false alarms cause harmful disorder depends critically on the interaction between spatial geometry, strategic behavior, and psychological limits—not merely on the alarm itself. |
| JEL: | C72 D61 K42 |
| Date: | 2025–05 |
| URL: | https://d.repec.org/n?u=RePEc:nbr:nberwo:33852 |
| By: | Yiyin Cao; Chuangyin Dang |
| Abstract: | A weakening of sequential rationality of sequential equilibrium yields Reny's (1992) weakly sequentially rational equilibrium (WSRE) in extensive-form games. WSRE requires Kreps and Wilson's (1982) consistent assessment to satisfy global rationality of nonconvex payoff functions at every information set reachable by a player's own strategy. The consistent assessment demands a convergent sequence of totally mixed behavioral strategy profiles and associated Bayesian beliefs. Nonetheless, due to the nonconvexity, proving the existence of WSRE required invoking the existence of a normal-form perfect equilibrium, which is sufficient but not necessary. Furthermore, Reny's WSRE definition does not fully specify how to construct the convergent sequence. To overcome these challenges, this paper develops a characterization of WSRE through $\varepsilon$-perfect $\gamma$-WSRE with local sequential rationality, which is accomplished by incorporating an extra behavioral strategy profile. For any given $\gamma>0$, we generate a perfect $\gamma$-WSRE as a limit point of a sequence of $\varepsilon_k$-perfect $\gamma$-WSRE with $\varepsilon_k\to 0$. A WSRE is then acquired from a limit point of a sequence of perfect $\gamma_q$-WSRE with $\gamma_q\to 0$. This characterization enables analytical identification of all WSREs in small extensive-form games and a direct proof of the existence of WSRE. An application of the characterization yields a polynomial system that serves as a necessary and sufficient condition for verifying whether a totally mixed assessment is an $\varepsilon$-perfect $\gamma$-WSRE. Exploiting the system, we devise differentiable path-following methods to compute WSREs by establishing the existence of smooth paths, which are secured from the equilibrium systems of barrier and penalty extensive-form games. Comprehensive numerical results further confirm the efficiency of the methods. |
| Date: | 2025–05 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2505.19496 |
| By: | Daniel Aronoff; Robert M. Townsend |
| Abstract: | We present a model of a market that is intermediated by broker-dealers where there is multiple equilibrium. We then design a smart-contract that receives messages and algorithmically sends trading instructions. The smart-contract resolves the multiple equilibrium by implementing broker-dealer joint profit maximization as a Nash equilibrium. This outcome relies upon several factors: Agent commitments to follow the smart contract protocol; selective privacy of information; a structured timing of trade offers and acceptances and, crucially, trust that the smart-contract will execute the correct algorithm. Commitment is achieved by a legal contract or contingent deposit that incentivizes agents to comply with the protocol. Privacy is maintained by using fully homomorphic encryption. Multiple equilibrium is resolved by imposing a sequential ordering of trade offers and acceptances, and trust in the smart-contract is achieved by appending the smart-contract to a public blockchain, thereby enabling verification of its computations. This model serves as an example of how a smart-contract implemented with cryptography and blockchain can improve market outcomes. |
| Date: | 2025–05 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2505.22940 |
| By: | Francesco Morri; H\'el\`ene Le Cadre; Pierre Gruet; Luce Brotcorne |
| Abstract: | We characterize zonal ancillary market coupling relying on noncooperative game theory. To that purpose, we formulate the ancillary market as a multi-leader single follower bilevel problem, that we subsequently cast as a generalized Nash game with side constraints and nonconvex feasibility sets. We determine conditions for equilibrium existence and show that the game has a generalized potential game structure. To compute market equilibrium, we rely on two exact approaches: an integrated optimization approach and Gauss-Seidel best-response, that we compare against multi-agent deep reinforcement learning. On real data from Germany and Austria, simulations indicate that multi-agent deep reinforcement learning achieves the smallest convergence rate but requires pretraining, while best-response is the slowest. On the economics side, multi-agent deep reinforcement learning results in smaller market costs compared to the exact methods, but at the cost of higher variability in the profit allocation among stakeholders. Further, stronger coupling between zones tends to reduce costs for larger zones. |
| Date: | 2025–05 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2505.03288 |
| By: | Suga, Nobuhito; Tawada, Makoto; Yanase, Akihiko |
| Keywords: | Government, Trade, Comparative advantage, Nash equilibrium, Symmetry-breaking, |
| Date: | 2025–05 |
| URL: | https://d.repec.org/n?u=RePEc:hok:dpaper:382 |
| By: | Songtao He; Erfang Shan; Xinyu Sun |
| Abstract: | B\'eal et al. (Int J Game Theory 54, 2025) introduce the Diversity Owen value for TU-games with diversity constraints, and provide axiomatic characterizations using the axioms of fairness and balanced contributions. However, there exist logical flaws in the proofs of the uniqueness of these characterizations. In this note we provides the corrected proofs of the characterizations by introducing the null player for diversity games axiom. Also, we establish two alternative characterizations of the Diversity Owen value by modified or weakening the axioms of the above characterizations. |
| Date: | 2025–05 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2505.24171 |
| By: | Lijun Bo; Yijie Huang; Xiang Yu |
| Abstract: | This paper studies the mean field game (MFG) problem arising from a large population competition in fund management, featuring a new type of relative performance via the benchmark tracking constraint. In the n-agent model, each agent can strategically inject capital to ensure that the total wealth outperforms the benchmark process, which is modeled as a linear combination of the population's average wealth process and an exogenous market index process. That is, each agent is concerned about the performance of her competitors captured by the floor constraint. With a continuum of agents, we formulate the constrained MFG problem and transform it into an equivalent unconstrained MFG problem with a reflected state process. We establish the existence of the mean field equilibrium (MFE) using the PDE approach. Firstly, by applying the dual transform, the best response control of the representative agent can be characterized in analytical form in terms of a dual reflected diffusion process. As a novel contribution, we verify the consistency condition of the MFE in separated domains with the help of the duality relationship and properties of the dual process. |
| Date: | 2025–05 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2505.01858 |
| By: | Bernhardt, Dan (Department of Economics, University of Illinois and Department of Economics, University of Warwick); Hwang, Ilwoo (Department of Economics, Seoul National University); Krasa, Stefan (Department of Economics, University of Illinois) |
| Abstract: | We modify a canonical two-agent bargaining game with investments in a joint project, by allowing agents to also invest in outside options that improve their bargaining positions. Absent outside options, it is well known that equal bargaining power maximizes output. However, this is no longer true when investment in outside options is possible and the joint-project technology exhibits stronger substitutability than Cobb-Douglas. When this is so, equal bargaining power minimizes project output while maximizing total investment in unused outside options. Paradoxically, when inputs are suffciently strong substitutes, starting at equal bargaining power, each agent would gain from reductions in their own bargaining power. |
| Keywords: | Bargaining ; bargaining power ; outside option ; hold-up problem JEL Codes: C78 ; D25 ; L24 |
| Date: | 2025 |
| URL: | https://d.repec.org/n?u=RePEc:wrk:warwec:1559 |
| By: | Guo, Qilin |
| Abstract: | Drawing on the broad historical trend of power decentralization, this paper proposes the Principle of Power Entropy Increase, introducing the concept of power entropy and its mathematical formulation to systematically illuminate the evolutionary shift of power structures from concentration to dispersion. Power entropy increase is framed as a natural response of social systems to the challenges of power scarcity, structural complexity, and governance pressure—serving as the underlying logic that drives the evolution of public governance toward democratic institutions. On this basis, the paper is the first to advance and rigorously substantiate the theoretical proposition that democracy is the inevitable trajectory of institutional evolution. It contends that democracy is not born of ideological design, but arises as a structurally optimal outcome driven by systemic dynamics—a Nash equilibrium in the context of generalized social games. This principle offers not only a new perspective on political modernization and institutional transition, but also a theoretical foundation and analytical tool for assessing and forecasting transformations in power structures. |
| Date: | 2025–05–30 |
| URL: | https://d.repec.org/n?u=RePEc:osf:socarx:5h4j2_v1 |
| By: | Thierry Warin |
| Abstract: | This article develops a Bayesian game-theoretic model to analyze the persistence and widespread prevalence of misinformation, disinformation, and malinformation within contemporary media ecosystems. Using the classic “Two Generals Problem” metaphor, we conceptualize information transmission as a strategic coordination game under conditions of uncertainty, emphasizing critical factors such as costs associated with truthful content production (??), reliability of message dissemination (?), payoffs for truthful versus misleading communication (?? , ?? ), audience composition (?), and algorithmic amplification (?). The model elucidates why actors, even those motivated by accuracy, rationally gravitate toward misinformation strategies when truthful messaging incurs significant costs and faces substantial barriers to audience penetration. Conditions under which honest signaling deteriorates are explicitly derived, and equilibrium outcomes—including both truthful and misinformation-dominated equilibria—are thoroughly analyzed. Historical and contemporary examples, such as Cold War disinformation operations, social media misinformation during the 2016 U.S. elections, COVID-19 pandemic misinformation, and deepfake technology applications, provide empirical validation. Our findings underscore the necessity of systemic interventions aimed at reducing truth-telling costs, enhancing message reliability, regulating algorithmic amplification, and restructuring incentives to facilitate transitions toward sustained truthful communication equilibria. Future research directions include empirical quantification of model parameters and exploring network effects to enhance policy relevance and effectiveness. Cet article développe un modèle bayésien de théorie des jeux pour analyser la persistance et la prévalence généralisée de la désinformation et de la malinformation dans les écosystèmes médiatiques contemporains. En utilisant la métaphore classique du « problème des deux généraux », nous concevons la transmission d'informations comme un jeu de coordination stratégique dans des conditions d'incertitude, en mettant l'accent sur des facteurs critiques tels que les coûts associés à la production d'un contenu véridique (??), la fiabilité de la diffusion des messages (?) et la fiabilité de l'information (?), la fiabilité de la diffusion des messages (?), les avantages d'une communication véridique par rapport à une communication trompeuse (?? , ?? ), la composition de l'audience (?) et l'amplification algorithmique (?). Le modèle explique pourquoi les acteurs, même ceux qui sont motivés par l'exactitude, s'orientent rationnellement vers des stratégies de désinformation lorsque les messages véridiques entraînent des coûts importants et se heurtent à des obstacles considérables à la pénétration de l'audience. Les conditions dans lesquelles la sincérité des signaux se détériore sont explicitement déduites, et les résultats d'équilibre - y compris les équilibres dominés par la vérité et la désinformation - sont analysés en profondeur. Des exemples historiques et contemporains, tels que les opérations de désinformation de la guerre froide, la désinformation sur les médias sociaux pendant les élections américaines de 2016, la désinformation sur la pandémie COVID-19 et les applications de la technologie deepfake, fournissent une validation empirique. Nos conclusions soulignent la nécessité d'interventions systémiques visant à réduire les coûts liés à l'établissement de la vérité, à renforcer la fiabilité des messages, à réglementer l'amplification algorithmique et à restructurer les incitations afin de faciliter l'établissement de la vérité. |
| Keywords: | Bayesian game-theoretic model, disinformation, reliability of information, modèle bayésien, théorie des jeux, désinformation, fiabilité de l'information |
| Date: | 2025–05–20 |
| URL: | https://d.repec.org/n?u=RePEc:cir:cirwor:2025s-13 |
| By: | Kiljae Lee; Ziqi Liu; Weijing Tang; Yuan Zhang |
| Abstract: | Data Shapley is an important tool for data valuation, which quantifies the contribution of individual data points to machine learning models. In practice, group-level data valuation is desirable when data providers contribute data in batch. However, we identify that existing group-level extensions of Data Shapley are vulnerable to shell company attacks, where strategic group splitting can unfairly inflate valuations. We propose Faithful Group Shapley Value (FGSV) that uniquely defends against such attacks. Building on original mathematical insights, we develop a provably fast and accurate approximation algorithm for computing FGSV. Empirical experiments demonstrate that our algorithm significantly outperforms state-of-the-art methods in computational efficiency and approximation accuracy, while ensuring faithful group-level valuation. |
| Date: | 2025–05 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2505.19013 |
| By: | Stelios Arvanitis (Department of Economics, AUEB) |
| Abstract: | Within the Frequentist Model Averaging framework for linear models, we introduce a multi-objective model averaging methodology that extends both the generalized Jackknife Model Averaging (JMA) and the Mallows Model Averaging (MMA) criteria. Our approach constructs estimators based on stochastic dominance principles and explores averaging methods that minimize multiple scalarizations of the joint criterion integrating MMA and JMA. Additionally, we propose an estimator that can be interpreted as a Nash bargaining solution between the competing scalar criteria. We establish the asymptotic properties of these estimators under both correct specification and global misspecification. Monte Carlo simulations demonstrate that some of the proposed averaging estimators outperform JMA and MMA in terms of MSE/MAE. In an empirical application to economic growth data, our model averaging methods assign greater weight to fundamental Solow-type growth variables while also incorporating regressors that capture the role of geography and institutional quality. |
| Keywords: | frequentistic model averaging, Jacknife MA, Mallows MA, multi-objective optimization, stochastic dominance, approximate bound, â„“p-scalarization, Nash bargaining solution, growth regressions |
| JEL: | C51 C52 |
| Date: | 2025–03 |
| URL: | https://d.repec.org/n?u=RePEc:qed:wpaper:1535 |
| By: | Felix Reichel |
| Abstract: | This paper examines strategic effort and positioning choices resulting in bandwagon effects under externalities in finite multi-stage games using causal evidence from triathlon (Reichel, 2025). Focusing on open-water swim draftingwhere athletes reduce drag most effectively by swimming directly behind peerswe estimate its performance effects through a structural contest framework with endogenous, deterministic effort and drafting position. Leveraging exogenous variation from COVID-19 drafting bans in Austrian triathlons, we apply a panel leave-one-out (LOO/LOTO) peer ability instrumental variables (IV) strategy to isolate the causal non-linear effect of drafting. Results from restricted sample analysis and pooled estimated bandwagon IV effects show substantial and nonlinear gains: in small (group size below 10) drafting swim groups/clusters, each deeper position improves finishing rank on average by over 30%, with rapidly diminishing returns in larger groups. Leading however is consistently more costly than optimal positioning, aligning with theoretical predictions of energy expenditure (metabolic costs). |
| Date: | 2025–05 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2505.03247 |