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on Game Theory |
| By: | Michel Grabisch (Centre d'Economie de la Sorbonne, Université Paris 1 Panthéon-Sorbonne, Paris School of Economics); Elena Parilina (Saint Peterburg State University); Agnieszka Rusinowska (Centre d'Economie de la Sorbonne, CNRS, Université Paris 1 Panthéon-Sorbonne, Paris School of Economics); Georges Zaccour (GERAD, HEC Montréal) |
| Abstract: | We investigate a T-stage dynamic network formation game with linear-quadratic payoffs. Players interact through network which they create as a result of their actions. We study two versions of the dynamic game and provide the equilibrium analysis. First, we assume that players sequentially propose links to others with whom they want to connect and choose the levels of contribution for their links. The players have limited total contributions or capacities for forming links at every stage which can differ among players and over time. They cannot delete links, but the principle of natural elimination of links with no contribution is adopted. Next, we assume that the players simultaneously and independently propose links to other players and have overall limited capacities for the whole game, and not for each stage. This means that every player can redistribute the capacity not only over links, but also over time. The equilibrium concept for the first version of the dynamic game is subgame perfect equilibrium, while it is the Nash equilibrium in open-loop strategies for the second version. Both models are illustrated with numerical examples |
| Keywords: | Network Formation Game; Dynamic Linear-Quadratic Game; Farsighted Players; Limited Capacities; Nash Equilibrium |
| JEL: | D85 C73 |
| Date: | 2025–07 |
| URL: | https://d.repec.org/n?u=RePEc:mse:cesdoc:25019 |
| By: | Dziubiński, M.; Goyal, S.; Zhou, J. |
| Abstract: | We study a two-player model of conflict with multiple battlefields – the novel element is that each of the players has their own network of spillovers so that resources allocated to one battle can be utilized in winning neighbouring battles. There exists a unique equilibrium in which the relative probability of a player winning a battle is the product of the ratio of the centrality of the battlefield in the two respective competing networks and the ratio of the relative cost of efforts of the two players. We study the design of networks and characterize networks that maximize total efforts and maximize total utility. Finally, we characterize the equilibrium of a game in which players choose both networks and efforts in the battles. |
| Date: | 2025–09–29 |
| URL: | https://d.repec.org/n?u=RePEc:cam:camjip:2525 |
| By: | Kevin He; Jonathan Libgober |
| Abstract: | We extend the indirect evolutionary approach to the selection of (possibly misspecified) models. Agents with different models match in pairs to play a stage game, where models define feasible beliefs about game parameters and about others' strategies. In equilibrium, each agent adopts the feasible belief that best fits their data and plays optimally given their beliefs. We define the stability of the resident model by comparing its equilibrium payoff with that of the entrant model, and provide conditions under which the correctly specified resident model can only be destabilized by misspecified entrant models that contain multiple feasible beliefs (that is, entrant models that permit inference). We also show that entrants may do well in their matches against the residents only when the entrant population is large, due to the endogeneity of misspecified beliefs. Applications include the selection of demand-elasticity misperception in Cournot duopoly and the emergence of analogy-based reasoning in centipede games. |
| Date: | 2025–09 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2509.16067 |
| By: | Francesco Caruso (Università di Napoli Federico II); Maria Carmela Ceparano (Università di Napoli Federico II); Federico Quartieri (Università di Napoli Federico II) |
| Abstract: | We examine a game-theoretic model of vessel sharing agreements in industries endowed with a general class of price functions and with classes of convex cost functions. We study the equilibrium structure thereof—in particular, the existence of a unique equilibrium aggregate and the existence of a unique equilibrium—and we provide a comparative statics analysis of consumer welfare with respect to an ordinal measure of concentration of the industry. We show that the a “high degree” of convexity of the cost functions can generate anti-competitive effects. In the presence of linear costs, the model satisfies a weak aggregative form in the sense of aggregative games. By allowing for the non-linearity of variable cost functions, we further weaken the aggregative nature of the games considered. Here we provide a specific new technique for treating these games in which both the equilibrium structure and the comparative statics analysis are based on the comparison of the equilibrium conditions of the players who positively vary their strategies within the groups that positively vary the group’s equilibrium aggregate from an equilibrium with a smaller global aggregate associated with a less concentrated industry to an equilibrium with a larger global aggregate associated with a more concentrated industry. |
| Keywords: | Vessel sharing agreements, Nash equilibrium uniqueness, Generalized concavity, Comparative statics, Welfare analysis. |
| Date: | 2025–09–11 |
| URL: | https://d.repec.org/n?u=RePEc:sef:csefwp:760 |
| By: | Natalie Collina; Surbhi Goel; Aaron Roth; Emily Ryu; Mirah Shi |
| Abstract: | Aligning AI systems with human values remains a fundamental challenge, but does our inability to create perfectly aligned models preclude obtaining the benefits of alignment? We study a strategic setting where a human user interacts with multiple differently misaligned AI agents, none of which are individually well-aligned. Our key insight is that when the users utility lies approximately within the convex hull of the agents utilities, a condition that becomes easier to satisfy as model diversity increases, strategic competition can yield outcomes comparable to interacting with a perfectly aligned model. We model this as a multi-leader Stackelberg game, extending Bayesian persuasion to multi-round conversations between differently informed parties, and prove three results: (1) when perfect alignment would allow the user to learn her Bayes-optimal action, she can also do so in all equilibria under the convex hull condition (2) under weaker assumptions requiring only approximate utility learning, a non-strategic user employing quantal response achieves near-optimal utility in all equilibria and (3) when the user selects the best single AI after an evaluation period, equilibrium guarantees remain near-optimal without further distributional assumptions. We complement the theory with two sets of experiments. |
| Date: | 2025–09 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2509.15090 |
| By: | Andrzej Baranski; Ernesto Reuben; Arno Riedl |
| Abstract: | In a laboratory experiment, we study the role of fairness ideals as focal points in coordination problems in homogeneous and heterogeneous groups. We elicit the normatively preferred behavior about how a subsequent coordination game should be played. In homogeneous groups, people share a unique fairness ideal how to solve the coordination problem, whereas in heterogeneous groups, multiple conflicting fairness ideals prevail. In the coordination game, homogeneous groups are significantly more likely than their heterogeneous counterparts to sustain efficient coordination. The reason is that homogeneous groups coordinate on the unique fairness ideal, whereas heterogeneous groups disagree on the fairness ideal to be played. In both types of groups, equilibria consistent with fairness ideals are most stable. Hence, the difference in coordination success between homogeneous and heterogeneous groups occurs because of the normative disagreement in the latter types of group, making it much harder to reach an equilibrium at a fairness ideal. |
| Keywords: | fairness ideals, focal points, coordination, cooperation, experiment |
| JEL: | H41 C92 D63 |
| Date: | 2025 |
| URL: | https://d.repec.org/n?u=RePEc:ces:ceswps:_12195 |
| By: | Delia Coculescu; Maximilian Janisch; Thomas Leh\'ericy |
| Abstract: | Pharmaceutical markets for life-saving therapies combine monopoly power with insurance coverage. We build a tractable sequential game in which a patent-holder chooses the drug price, a profit-maximising insurer sets its premium, and a population of heterogeneous agents decide whether to insure and, conditional on diagnosis, whether to purchase treatment. Two sufficient statistics - subjective illness probability and reservation price - capture heterogeneity and nest risk-aversion and liquidity-constraint motives within a unified framework. We prove existence of subgame-perfect Nash equilibria and show that entry of an insurer strictly raises producer profits but may raise or lower both drug prices and treatment uptake, depending on the joint distribution of the population statistics. Numerical experiments calibrated to flexible parametric families illustrate non-monotone comparative statics and quantify conditions under which insurance reduces access. Our results provide benchmarks for evaluating price negotiations, price caps, and subsidy schemes in high-cost drug markets. |
| Date: | 2025–09 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2509.16125 |
| By: | Olivier Bochet (Division of Social Science, New York University Abu Dhabi; Center for Behavioral Institutional Design (C-BID), New York University Abu Dhabi); Mathieu Faure (Aix-Marseille Univ., CNRS, AMSE, Marseille, France); Yan Long (Huazhong University of Science and Technology, China); Yves Zenou (Monash University, Australia, and CEPR) |
| Abstract: | In contrast to standard economic models, recent empirical evidence suggests that agents often operate based on subjective and divergent views of the competitive landscape. We develop a novel framework in which such imperfections are explicitly modeled through subjective perception networks, and introduce the concept of perception-consistent equilibrium (PCE), in which agents' actions and conjectures respond to the feedback generated by perceived competition. We establish the existence of equilibrium in broad classes of aggregative games. The model typically yields multiple equilibria, including outcomes that feature patterns of localized exclusion. Remarkably, heterogeneity in beliefs induces perceived competition rents-payoff differentials that arise purely from subjective misperceptions. We further show that PCE actions correspond to ordinal centrality measures, with eigenvector centrality emerging as a behavioral benchmark in separable payoff environments. Finally, a graph-theoretic taxonomy of PCEs reveals a hierarchical structure that ranks perceived competition rents. We also give conditions under which a unique stable equilibrium exists. |
| Keywords: | competition, perception-consistent equilibrium, exclusionary equilibria, bounded rationality, ordinal centrality, eigenvector centrality, perceived competition rent |
| JEL: | C72 D43 Z13 |
| Date: | 2025–10 |
| URL: | https://d.repec.org/n?u=RePEc:aim:wpaimx:2515 |
| By: | Din Amir; Bar Hoter; Moran Koren |
| Abstract: | This study examines strategic behavior in crowdfunding using a large-scale online experiment. Building on the model of Arieli et. al 2023, we test predictions about risk aversion (i.e., opting out despite seeing a positive private signal) and mutual insurance (i.e., opting in despite seeing a negative private signal) in a static, single-shot crowdfunding game, focusing on informational incentives rather than dynamic effects. Our results validate key theoretical predictions: crowdfunding mechanisms induce distinct strategic behaviors compared to voting, where participants are more likely to follow private signals (odds ratio: 0.139, $p |
| Date: | 2025–10 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2510.14872 |
| By: | Mohamed Bahlali (Aix-Marseille Univ., CNRS, AMSE, Marseille, France); Raouf Boucekkine (Aix-Marseille Univ., CNRS, AMSE, Marseille, France); Quentin Petit (EDF & FiME Lab, Paris, France) |
| Abstract: | We propose a mean-field game (MFG) set-up to study the dynamics of spatial agglomeration in a continuous space-time framework where trade across locations may follow a broad class of static gravity models. Forward-looking intertemporal utility-maximizing agents work and migrate in a twodimensional geography and face idiosyncratic shocks. Equilibrium wages and prices depend on their common distribution and adjust statically according to the underlying trade model. We first prove existence and uniqueness of the static trade equilibrium. We then prove existence of dynamic equilibria. In the case of Krugman (1996)'s racetrack economy, we obtain closed-form solutions for small sinusoidal perturbations around the steady state, and we identify the sets of parameters that lead to agglomeration or dispersion. We exploit the MFG structure of the model to explicitly quantify how uncertainty and forward-looking expectations contribute to agglomeration and dispersion. In particular, we show that, regardless of the static trade model, forward-looking expectations always promote agglomeration, but cannot reverse the dominant pattern that would arise under myopic behavior. |
| Date: | 2025–10 |
| URL: | https://d.repec.org/n?u=RePEc:aim:wpaimx:2517 |
| By: | Chenlan Wang; Jimin Han; Diana Jue-Rajasingh |
| Abstract: | This paper develops a game-theoretic model and an agent-based model to study group formation driven by resource pooling, spatial cohesion, and heterogeneity. We focus on cross-sector partnerships (CSPs) involving public, private, and nonprofit organizations, each contributing distinct resources. Group formation occurs as agents strategically optimize their choices in response to others within a competitive setting. We prove the existence of stable group equilibria and simulate formation dynamics under varying spatial and resource conditions. The results show that limited individual resources lead to groups that form mainly among nearby actors, while abundant resources allow groups to move across larger distances. Increased resource heterogeneity and spatial proximity promote the formation of larger and more diverse groups. These findings reveal key trade-offs shaping group size and composition, guiding strategies for effective cross-sector collaborations and multi-agent systems. |
| Date: | 2025–09 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2509.18551 |
| By: | Masaaki Fujii |
| Abstract: | In this work, we combine the mean-field game theory with the classical idea of binomial tree framework, pioneered by Sharpe and Cox, Ross & Rubinstein, to solve the equilibrium price formation problem for the stock. For agents with exponential utilities and recursive utilities of exponential type, we prove the existence of a unique mean-field equilibrium and derive an explicit formula for equilibrium transition probabilities of the stock price by restricting its trajectories onto a binomial tree. The agents are subject to stochastic terminal liabilities and incremental endowments, both of which are dependent on unhedgeable common and idiosyncratic factors, in addition to the stock price path. Finally, we provide numerical examples to illustrate the qualitative effects of these components on the equilibrium price distribution. |
| Date: | 2025–10 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2510.11261 |
| By: | Ala Avoyan; Daniela Valdivia |
| Abstract: | The paper examines how the timing of decisions shapes outcomes in coordination settings. Theoretically, the outcomes become predictable and efficient when decisions are made sequentially rather than simultaneously. Our experimental evidence shows that sequential moves promote remarkably high efficiency, and these effects are far less sensitive to increased group size. A key finding is that the sequential structure alters the distribution of strategic uncertainty in a group, aggregating it and allocating most of it to the first mover. Dynamic measures further reveal that coordination failures under simultaneous moves stem from weak resilience to setbacks rather than fragility of equilibria. |
| Keywords: | strategic uncertainty, order of moves, experiment |
| JEL: | C72 D81 C92 |
| Date: | 2025 |
| URL: | https://d.repec.org/n?u=RePEc:ces:ceswps:_12198 |
| By: | Paul S. Koh (Yonsei University) |
| Abstract: | Market definition holds significant importance in antitrust cases, yet achieving consensus on the correct approach remains elusive. As a result, analysts routinely entertain multiple market definitions to ensure the resilience of their conclusions. I propose a simple framework for conducting organized sensitivity analysis with respect to market definition. I model candidate market definitions as partially ordered and use a Hasse diagram, a directed acyclic graph representing a finite partial order, to summarize the sensitivity analysis. I use the Shapley value and the Shapley-Shubik power index to quantify the average marginal contribution of each firm in driving the conclusion. I illustrate the method's usefulness with an application to the Albertsons/Safeway (2015) merger. |
| Keywords: | Market definition, sensitivity analysis, partial order, Hasse diagram, Shapley value |
| Date: | 2025–08 |
| URL: | https://d.repec.org/n?u=RePEc:yon:wpaper:2025rwp-262 |
| By: | Shuige Liu |
| Abstract: | We examine how misinformation spreads in social networks composed of individuals with long-term offline relationships. Especially, we focus on why misinformation persists and diffuses despite being recognized by most as false. In our psychological game theoretical model, each agent who receives a piece of (mis)information must first decide how to react -- by openly endorsing it, remaining silent, or openly challenging it. After observing the reactions of her neighbors who also received the message, the agent then chooses whether to forward it to others in her own chatroom who have not yet received it. By distinguishing these two roles, our framework addresses puzzling real-world phenomena, such as the gap between what individuals privately believe and what they publicly transmit. A key assumption in our model is that, while perceived veracity influences decisions, the dominant factor is the alignment between an agent's beliefs and those of her social network -- a feature characteristic of communities formed through long-term offline relationships. This dynamic can lead agents to tacitly accept and even propagate information they privately judge to be of low credibility. Our results challenge the view that improving information literacy alone can curb the spread of misinformation. We show that when agents are highly sensitive to peer pressure and the network exhibits structural polarization, even if the majority does not genuinely believe in it, the message still can spread widely without encountering open resistance. |
| Date: | 2025–10 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2510.08658 |