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on Game Theory |
| By: | Simon Martin; Hans-Theo Normann; Paul Püplichhuisen; Tobias Werner |
| Abstract: | We study the propensity of independent algorithms to collude in repeated Cournot duopoly games. Specifically, we investigate the predictive power of different oligopoly and bargaining solutions regarding the effect of asymmetry between firms. We find that both consumers and firms can benefit from asymmetry. Algorithms produce more competitive outcomes when firms are symmetric, but less when they are very asymmetric. Although the static Nash equilibrium underestimates the effect on total quantity and overestimates the effect on profits, it delivers surprisingly accurate predictions in terms of total welfare. The best description of our results is provided by the equal relative gains solution. In particular, we find algorithms to agree on profits that are on or close to the Pareto frontier for all degrees of asymmetry. Our results suggest that the common belief that symmetric industries are more prone to collusion may no longer hold when algorithms increasingly drive managerial decisions. |
| Keywords: | algorithmic collusion, Cournot duopoly, asymmetric firms |
| JEL: | C73 D43 L13 |
| Date: | 2025 |
| URL: | https://d.repec.org/n?u=RePEc:ces:ceswps:_11629 |
| By: | Eric Bahel (Department of Economics, Virginia Polytechnic Institute and State University); Christian Trudeau (Department of Economics, University of Windsor); Haoyu Wang (Department of Economics, Virginia Polytechnic Institute and State University) |
| Abstract: | We introduce the notion of preconvexity, which extends the familiar concept of convexity found in cooperative games with transferable utility. In a convex game, the larger the group joined by an agent, the larger the marginal value brought to the group by that agent. By contrast, in strictly preconvex games, an agent's marginal contribution is initially decreasing (when joining small groups), and it eventually becomes increasing at (and above) some critical group size. As a consequence, the core of a preconvex game may be empty. Defining the property of semicohesiveness (related to marginal contributions at this critical group size), we prove that it is sufficient to guarantee a nonempty core. We also propose a new solution for the set of preconvex games; and we characterize this solution by combining three axioms which are natural in our framework. A stronger cohesiveness property (guaranteeing that our solution falls in the core) is also studied. Some additional results are provided for the special case of anticonvex games, for which marginal contributions are always non-increasing. |
| Keywords: | cooperation; allocation; core; preconvexity; cohesiveness. |
| JEL: | C71 D63 |
| Date: | 2025–02 |
| URL: | https://d.repec.org/n?u=RePEc:wis:wpaper:2501 |
| By: | Ian Ball; Xin Gao |
| Abstract: | We consider a sender--receiver game in which the state is multidimensional and the receiver's action is binary. The sender always prefers the same action. The receiver can select one dimension of the state to verify. Despite the extreme conflict of interest, costless communication can be influential. We identify a class of symmetric equilibria in which the sender's message reveals which dimensions of the state are highest, and the receiver selects one of these dimensions to check. Using this construction, we characterize whether the sender benefits from communication. Similar equilibria exist when the receiver can check multiple dimensions. |
| Date: | 2025–01 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2501.09875 |
| By: | Faisal Shah Khan; Norbert M. Linke; Anton Trong Than; Dror Baron |
| Abstract: | Quantum games, like quantum algorithms, exploit quantum entanglement to establish strong correlations between strategic player actions. This paper introduces quantum game-theoretic models applied to trading and demonstrates their implementation on an ion-trap quantum computer. The results showcase a quantum advantage, previously known only theoretically, realized as higher-paying market Nash equilibria. This advantage could help uncover alpha in trading strategies, defined as excess returns compared to established benchmarks. These findings suggest that quantum computing could significantly influence the development of financial strategies. |
| Date: | 2025–01 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2501.17189 |
| By: | René van den Brink (VU University Amsterdam and Tinbergen Institute); Agnieszka Rusinowska (CES - Centre d'économie de la Sorbonne - UP1 - Université Paris 1 Panthéon-Sorbonne - CNRS - Centre National de la Recherche Scientifique, CNRS - Centre National de la Recherche Scientifique, UP1 - Université Paris 1 Panthéon-Sorbonne, PSE - Paris School of Economics - UP1 - Université Paris 1 Panthéon-Sorbonne - ENS-PSL - École normale supérieure - Paris - PSL - Université Paris Sciences et Lettres - EHESS - École des hautes études en sciences sociales - ENPC - École nationale des ponts et chaussées - CNRS - Centre National de la Recherche Scientifique - INRAE - Institut National de Recherche pour l’Agriculture, l’Alimentation et l’Environnement) |
| Abstract: | This paper aims to connect the social network literature on centrality measures with the economic literature on von Neumann-Morgenstern expected utility functions using cooperative game theory. The social network literature studies various concepts of network centrality, such as degree, betweenness, connectedness, and so on. This resulted in a great number of network centrality measures, each measuring centrality in a different way. In this paper, we aim to explore which centrality measures can be supported as von Neumann-Morgenstern expected utility functions, reflecting preferences over different network positions in different networks. Besides standard axioms on lotteries and preference relations, we consider neutrality to ordinary risk. We show that this leads to a class of centrality measures that is fully determined by the degrees (i.e. the numbers of neighbours) of the positions in a network. Although this allows for externalities, in the sense that the preferences of a position might depend on the way how other positions are connected, these externalities can be taken into account only by considering the degrees of the network positions. Besides bilateral networks, we extend our result to general cooperative TU-games to give a utility foundation of a class of TU-game solutions containing the Shapley value. |
| Keywords: | group decisions and negotiations, weighted graph, degree centrality, von Neumann-Morgenstern expected utility function, cooperative game |
| Date: | 2024–12 |
| URL: | https://d.repec.org/n?u=RePEc:hal:pseptp:halshs-04188289 |
| By: | Pierre Bernhard (MACBES Team, INRIA Center of Université Côte d'Azur, Sophia Antipolis, France); Romain Biard (Université Marie et Louis Pasteur, CNRS, LmB, F-25000 Besançon, France); Marc Deschamps (Université Marie et Louis Pasteur, CRESE, UR3190, F-25000 Besançon, France) |
| Abstract: | There exist situations where firms (identical or not) are in a state of renewed interaction and where, at each period, in addition to exits, new firms (identical or not) may arrive. In such cases, no one is able to know ex ante exactly how many firms there will be in each period. One of the questions an incumbent firm might therefore ask itself, in this context, is what expected payoff it can expect. Our paper aims to provide an answer to this question, in finite and infinite horizons, using a discrete-time dynamic game with random arrival(s) and exit(s) of different types of firm(s). We first propose a general model, which we then particularize by considering the types as composed of identical players. Within this framework, we address the case of a dynamic Cournot oligopoly with sticky prices, and provide numerical illustrations to underline the interest of this approach and demonstrate its operational character. |
| Keywords: | Oligopoly, Random entries and exits, Types, Dynamic equilibirum, Cournot, sticky prices. |
| JEL: | C73 D43 L13 |
| Date: | 2025–01 |
| URL: | https://d.repec.org/n?u=RePEc:crb:wpaper:2025-01 |
| By: | Isabel Melguizo (Department of Economics, CIDE); Sergio Tovar (Department of Economics, CIDE) |
| Abstract: | We study a model in which individuals, that are heterogeneous along a single dimension capturing productivity, choose which of two available groups to join and how much costly effort to exert within their chosen group. On the one hand, individuals like to be in groups in which others' average performance is high (global quality). On the other hand, individuals are concerned with their ranking with respect to their peers' average performance (local standing). Nash equilibrium efforts are such that the higher the individual's productivity the higher her private outcome. In contrast, it is not necessarily the case that highly productive individuals exert more effort. Nash equilibrium efforts are never efficient and whether they are higher or lower than efficient efforts, depends on the strength of global quality versus local standing concerns. Stable partitions of the society into groups may either resemble grouping by productivity or productivity mixing. In contrast, efficient partitions must always exhibit grouping by productivity. |
| Keywords: | peer groups, segregation, mixing, effort choices, welfare |
| JEL: | D61 D60 Z13 |
| Date: | 2025–02 |
| URL: | https://d.repec.org/n?u=RePEc:emc:wpaper:dte646 |
| By: | Roberto Galbiati (ECON - Département d'économie (Sciences Po) - Sciences Po - Sciences Po - CNRS - Centre National de la Recherche Scientifique); Emeric Henry (Institut d'Études Politiques [IEP] - Paris); Nicolas Jacquemet (PSE - Paris School of Economics - UP1 - Université Paris 1 Panthéon-Sorbonne - ENS-PSL - École normale supérieure - Paris - PSL - Université Paris Sciences et Lettres - EHESS - École des hautes études en sciences sociales - ENPC - École des Ponts ParisTech - CNRS - Centre National de la Recherche Scientifique - INRAE - Institut National de Recherche pour l’Agriculture, l’Alimentation et l’Environnement, CES - Centre d'économie de la Sorbonne - UP1 - Université Paris 1 Panthéon-Sorbonne - CNRS - Centre National de la Recherche Scientifique) |
| Abstract: | Formal enforcement punishing defectors can sustain cooperation by changing incentives. In this paper, we introduce a second effect of enforcement: it can also affect the capacity to learn about the group's cooperativeness. Indeed, in contexts with strong enforcement, it is difficult to tell apart those who cooperate because of the threat of fines from those who are intrinsically cooperative types. Whenever a group is intrinsically cooperative, enforcement will thus have a negative dynamic effect on cooperation because it slows down learning about prevalent values in the group that would occur under a weaker enforcement. We provide theoretical and experimental evidence in support of this mechanism. Using a lab experiment with independent interactions and random rematching, we observe that, in early interactions, having faced an environment with fines in the past decreases current cooperation. We further show that this results from the interaction between enforcement and learning: the effect of having met cooperative partners has a stronger effect on current cooperation when this happened in an environment with no enforcement. Replacing one signal of deviation without fine by a signal of cooperation without fine in a player's history increases current cooperation by 10%; while replacing it by a signal of cooperation with fine increases current cooperation by only 5%. |
| Keywords: | Enforcement, social values, cooperation, learning, spillovers, repeated games, experiments |
| Date: | 2024–03 |
| URL: | https://d.repec.org/n?u=RePEc:hal:pseptp:hal-04511257 |
| By: | Nicolas Jacquemet (PSE - Paris School of Economics - UP1 - Université Paris 1 Panthéon-Sorbonne - ENS-PSL - École normale supérieure - Paris - PSL - Université Paris Sciences et Lettres - EHESS - École des hautes études en sciences sociales - ENPC - École nationale des ponts et chaussées - CNRS - Centre National de la Recherche Scientifique - INRAE - Institut National de Recherche pour l’Agriculture, l’Alimentation et l’Environnement, CES - Centre d'économie de la Sorbonne - UP1 - Université Paris 1 Panthéon-Sorbonne - CNRS - Centre National de la Recherche Scientifique); Stéphane Luchini; Jason Shogren; Adam Zylbersztejn |
| Abstract: | Under incomplete contracts, the mutual belief in reciprocity facilitates how traders create value through economic exchange. Creating such beliefs among strangers can be challenging even when they are allowed to communicate, because communication is cheap. In this paper, we first extend the literature showing that a truth-telling oath increases honesty to a sequential trust game with pre-play, fixed-form, and cheap-talk communication. Our results confirm that the oath creates more trust and cooperative behavior thanks to an improvement in communication; but we also show that the oath induces selection into communication -it makes people more wary of using communication, precisely because communication speaks louder under oath. We next designed additional treatments featuring mild and deterrent fines for deception to measure the monetary equivalent of the non-monetary incentives implemented by a truth-telling oath. We find that the oath is behaviorally equivalent to mild fines. The deterrent fine induces the highest level of cooperation. Altogether, these results confirm that allowing for interactions under oath within a trust game with communication creates significantly more economic value than the identical exchange institutions without the oath. |
| Keywords: | Trust game, cooperation, communication, commitment, deception, fine, oath |
| Date: | 2024 |
| URL: | https://d.repec.org/n?u=RePEc:hal:pseptp:halshs-04722343 |
| By: | Michele Crescenzi |
| Abstract: | We compare two procedures for the iterated removal of strictly dominated strategies. In the nested procedure, a strategy of a player is removed only if it is dominated by an unremoved strategy. The universal procedure is more comprehensive for it allows the removal of strategies that are dominated by previously removed ones. Outside the class of finite games, the two procedures may lead to different outcomes in that the universal one is always order independent while the other is not. Here we provide necessary and sufficient conditions for the equivalence of the two procedures. The conditions we give are variations of the bounded mechanisms from the literature on full implementation. The two elimination procedures are shown to be equivalent in quasisupermodular games as well as in games with compact strategy spaces and upper semicontinuous payoff functions. We show by example that order independence of the nested procedure is not sufficient for its being equivalent to the universal one. |
| Date: | 2025–01 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2501.17685 |
| By: | Emeline Bezin (PSE - Paris School of Economics - UP1 - Université Paris 1 Panthéon-Sorbonne - ENS-PSL - École normale supérieure - Paris - PSL - Université Paris Sciences et Lettres - EHESS - École des hautes études en sciences sociales - ENPC - École nationale des ponts et chaussées - CNRS - Centre National de la Recherche Scientifique - INRAE - Institut National de Recherche pour l’Agriculture, l’Alimentation et l’Environnement, PJSE - Paris Jourdan Sciences Economiques - UP1 - Université Paris 1 Panthéon-Sorbonne - ENS-PSL - École normale supérieure - Paris - PSL - Université Paris Sciences et Lettres - EHESS - École des hautes études en sciences sociales - ENPC - École nationale des ponts et chaussées - CNRS - Centre National de la Recherche Scientifique - INRAE - Institut National de Recherche pour l’Agriculture, l’Alimentation et l’Environnement); Bastien Chabé-Ferret (Middlesex University); David de la Croix (UCL - Université Catholique de Louvain = Catholic University of Louvain) |
| Abstract: | Fertility becomes a strategic choice for minorities when having a larger share of the population helps to increase power. If parents invest resources to educate their children, then raising fertility for strategic reasons might be at the cost of future human capital. We dispel this view using census data from several developing countries. We show that religious and ethnic minorities in Indonesia, China, and Malaysia tend to invest more in both education and fertility compared to larger groups. Solving for the Nash equilibrium of an appropriation game between two groups with education and fertility being prescribed as group-specific behavioral norms, we offer a rationale for the observed patterns provided that human capital is an important input to appropriation. |
| Keywords: | Human Capital, Nash equilibrium, Indonesia, Fertility, Quality-quantity trade-off, Minorities, Conflict, Population engineering |
| Date: | 2025 |
| URL: | https://d.repec.org/n?u=RePEc:hal:pseptp:hal-04877862 |
| By: | Joep van Sloun |
| Abstract: | This paper examines games with strategic complements or substitutes and incomplete information, where players are uncertain about the opponents' parameters. We assume that the players' beliefs about the opponent's parameters are selected from some given set of beliefs. One extreme is the case where these sets only contain a single belief, representing a scenario where the players' actual beliefs about the parameters are commonly known among the players. Another extreme is the situation where these sets contain all possible beliefs, representing a scenario where the players have no information about the opponents' beliefs about parameters. But we also allow for intermediate cases, where these sets contain some, but not all, possible beliefs about the parameters. We introduce an assumption of weakly increasing differences that takes both the choice belief and parameter belief of a player into account. Under this assumption, we demonstrate that greater choice-parameter beliefs leads to greater optimal choices. Moreover, we show that the greatest and least point rationalizable choice of a player is increasing in their parameter, and these can be determined through an iterative procedure. In each round of the iterative procedure, the lowest surviving choice is optimal for the lowest choice-parameter belief, while the greatest surviving choice is optimal for the highest choice-parameter belief. |
| Date: | 2025–01 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2501.15548 |
| By: | Joep van Sloun |
| Abstract: | This paper revisits the Hotelling model with waiting costs Kohlberg (1983), focusing on two specific settings where pure Nash equilibria do not exist: the asymmetric model with two firms and the symmetric model with three firms. In the asymmetric two-firm model, we show that the weaker concept of point rationalizability has strong predictive power, as it selects exactly two locations for both firms. As the two firms become more similar in their efficiency in handling queues of consumers, the two point rationalizable locations converge towards the center of the line. In the symmetric three-firm model, the set of point rationalizable choices forms an interval. This interval is shrinking in the inefficiency levels of the firms in handling queues of consumers. |
| Date: | 2025–01 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2501.15545 |
| By: | Sheyan Lalmohammed |
| Abstract: | The integration of artificial intelligence (AI) into economic systems represents a transformative shift in decision-making frameworks, introducing novel dynamics between human and AI agents. This paper proposes a welfare model that incorporates both game-theoretic and behavioral dimensions to optimize interactions within human-AI ecosystems. By leveraging agent-based modeling (ABM), we simulate these interactions, accounting for trust evolution, perceived risks, and cognitive costs. The framework redefines welfare as the aggregate utility of interactions, adjusted for collaboration synergies, efficiency penalties, and equity considerations. Dynamic trust is modeled using Bayesian updating mechanisms, while synergies between agents are quantified through a collaboration index rooted in cooperative game theory. Results reveal that trust-building and skill development are pivotal to maximizing welfare, while sensitivity analyses highlight the trade-offs between AI complexity, equity, and efficiency. This research provides actionable insights for policymakers and system designers, emphasizing the importance of equitable AI adoption and fostering sustainable human-AI collaborations. |
| Date: | 2025–01 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2501.15317 |
| By: | Huisheng Wang; H. Vicky Zhao |
| Abstract: | In financial markets, agents often mutually influence each other's investment strategies and adjust their strategies to align with others. However, there is limited quantitative study of agents' investment strategies in such scenarios. In this work, we formulate the optimal investment differential game problem to study the mutual influence among agents. We derive the analytical solutions for agents' optimal strategies and propose a fast algorithm to find approximate solutions with low computational complexity. We theoretically analyze the impact of mutual influence on agents' optimal strategies and terminal wealth. When the mutual influence is strong and approaches infinity, we show that agents' optimal strategies converge to the asymptotic strategy. Furthermore, in general cases, we prove that agents' optimal strategies are linear combinations of the asymptotic strategy and their rational strategies without others' influence. We validate the performance of the fast algorithm and verify the correctness of our analysis using numerical experiments. This work is crucial to comprehend mutual influence among agents and design effective mechanisms to guide their strategies in financial markets. |
| Date: | 2025–01 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2501.14259 |
| By: | Nigus, Halefom; Mohnen, Pierre (RS: GSBE other - not theme-related research, QE Econometrics); Nillesen, Eleonora (RS: GSBE UM-BIC, Maastricht Graduate School of Governance, RS: GSBE MGSoG); Di Falco, S. |
| Abstract: | Using two lab-in-the-field experiments, we study whether initial transgression promote subsequent anti-social behavior. In the first stage subjects participated in an experimental market game. In the second stage, subjects were given an opportunity to participate in antisocial experiment. We find that subjects who impose a negative externality on uninvolved third parties in the market game are also more likely to burn their partner's income in the second experiment. This finding is consistent with a conscience-numbing effect but could possibly also be explained by participants' preferences for consistency. |
| JEL: | C93 D03 D62 D63 M14 |
| Date: | 2023–08–14 |
| URL: | https://d.repec.org/n?u=RePEc:unm:unumer:2023027 |
| By: | Takashi Kunimoto; Rene Saran; Roberto Serrano |
| Abstract: | When the normative goals for a set of agents can be summarized in a set-valued rule and agents take actions that are rationalizable, a new theory of incentives emerges in which standard Bayesian incentive compatibility (BIC) is relaxed significantly. The paper studies the interim rationalizable implementation of social choice sets with a Cartesian product structure, a leading example thereof being ex-post efficiency. Setwise incentive compatibility (setwise IC), much weaker than BIC, is shown to be necessary for implementation. Setwise IC enforces incentives flexibly within the entire correspondence, instead of the pointwise enforcement entailed by BIC. Sufficient conditions, while based on the existence of SCFs in the correspondence that make truthful revelation a dominant strategy, are shown to be permissive to allow the implementation of ex-post efficiency in many settings where equilibrium implementation fails (e.g., bilateral trading, multidimensional signals). Furthermore, this success comes at little cost: all our mechanisms are well behaved, in the sense that best responses always exist. |
| Date: | 2025 |
| URL: | https://d.repec.org/n?u=RePEc:bro:econwp:2025-001 |
| By: | Yohei Mitani; Nobuyuki Hanaki |
| Abstract: | We conduct an online donation dictator game experiment with over 1, 300 participants, representative of the Japanese population, to investigate the relationship between the incentive scheme and prosocial behavior by systematically varying the stake size and probability of being paid, including those where the expected payments are controlled. We find that stake size is the main driver of donation decisions, even in the hypothetical scenario. Our result suggests that paying a large amount to a few participants incentivizes donation decisions better than paying a small amount to many in large-scale online experiments Creation-Date: 2025-2 |
| URL: | https://d.repec.org/n?u=RePEc:dpr:wpaper:1273 |
| By: | Seiya Hirano |
| Abstract: | In the adoption decisions of network goods, coordination problems lead to multiple equilibria. While consumers coordination significantly impacts the firm's pricing strategies, the precise relationship between coordination behavior and optimal pricing has received little attention. This paper analyzes optimal pricing strategies for network goods under different forms of consumer coordination in a two-period model with strategic consumers. We introduce two novel coordination criteria: risk dominance and threshold coordination. Risk dominance coordination accounts for the risk premium of no-adoption and threshold coordination accounts for consumer heterogeneity in the adoption of the good. We show that under the risk dominance criterion, the firm sets a lower price in period 1 when the risk of the coordination failure is high, but sets a higher price in period 1 when the risk is low. Under threshold coordination, the firm sets a lower price in period 1 when consumers hold pessimistic beliefs about the network size and sets a higher price in period 1 when beliefs are optimistic. Our findings highlight the critical implications of consumer coordination for firms' pricing strategies. |
| Date: | 2024–11 |
| URL: | https://d.repec.org/n?u=RePEc:dpr:wpaper:1267r |
| By: | Aditi Godbole; Zubin Shah; Ranjeet S. Mudholkar |
| Abstract: | This paper analyzes the 1/3 Financial Rule, a method of allocating income equally among debt repayment, savings, and living expenses. Through mathematical modeling, game theory, behavioral finance, and technological analysis, we examine the rule's potential for supporting household financial stability and reducing bankruptcy risk. The research develops theoretical foundations using utility maximization theory, demonstrating how equal allocation emerges as a solution under standard economic assumptions. The game-theoretic analysis explores the rule's effectiveness across different household structures, revealing potential strategic advantages in financial decision-making. We investigate psychological factors influencing financial choices, including cognitive biases and neurobiological mechanisms that impact economic behavior. Technological approaches, such as AI-driven personalization, blockchain tracking, and smart contract applications, are examined for their potential to support financial planning. Empirical validation using U.S. Census data and longitudinal studies assesses the rule's performance across various household types. Stress testing under different economic conditions provides insights into its adaptability and resilience. The research integrates mathematical analysis with behavioral insights and technological perspectives to develop a comprehensive approach to household financial management. |
| Date: | 2025–01 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2501.15557 |