nep-gth New Economics Papers
on Game Theory
Issue of 2024‒04‒15
twenty-one papers chosen by
Sylvain Béal, Université de Franche-Comté

  1. Bayesian Nash equilibrium in all-pay auctions with interdependent types By Ori Haimanko
  2. Market Exit and Minimax Regret By Gisèle Umbhauer
  3. Compellingness in Nash Implementation By Chatterji, Shurojit; Kunimoto, Takashi; Salles Ramos, Paulo Daniel
  4. The Indoctrination Game By David Lagziel; Lotem Ikan
  5. Nash Equilibria in Two-Resource Congestion Games with Player-Specific Payoff Functions By Fatima Khanchouche; Samir Sbabou; Hatem Smoui; Abderrahmane Ziad
  6. Status Consumption in Networks: A Reference Dependent Approach By Bramoullé, Y.; Ghiglino, C.
  7. Elimination Games By Aner Sela
  8. Axiomatic Approach to Farsighted Coalition Formation By Mert Kimya
  9. Risk-Sensitive Mean Field Games with Common Noise: A Theoretical Study with Applications to Interbank Markets By Xin Yue Ren; Dena Firoozi
  10. Interconnected Conflict By Dziubiński, M.; Goyal, S.; Zhou, J.
  11. Product Design in a Cournot Duopoly By Daniel;
  12. Language-based game theory in the age of artificial intelligence By Valerio Capraro; Roberto Di Paolo; Matjaz Perc; Veronica Pizziol
  13. Player strength and effort in contests By Giebe, Thomas; Gürtler, Oliver
  14. Second Opinions and the Humility Threshold By David Lagziel; Yevgeny Tsodikovich
  15. Algorithmic Collusion and Price Discrimination: The Over-Usage of Data By Zhang Xu; Mingsheng Zhang; Wei Zhao
  16. Learning to cooperate in the shadow of the law By Roberto Galbiati; Emeric Henry; Nicolas Jacquemet
  17. The impact of social status on the formation of collaborative ties and effort provision: An experimental study By Gergely Horvath; Mofei Jia
  18. Experimental Evidence on the Relation Between Network Centrality and Individual Choice By Choi, S.; Goyal, S.; Guo, F.; Moisan, F.
  19. Competing Mechanisms in Games Played Through Agents: Theory and Experiment By Seungjin Han; Andrew Leal
  20. Equitable Pricing in Auctions By Simon Finster; Patrick Loiseau; Simon Mauras; Mathieu Molina; Bary Pradelski
  21. All-Pay Matching Contests By Aner Sela

  1. By: Ori Haimanko (BGU)
    Keywords: All-pay auctions, incomplete information, behavioral strategies, Bayesian Nash equilibrium, interdependent types.
    JEL: C72 D44 D82
    Date: 2023
  2. By: Gisèle Umbhauer (BETA - Bureau d'Économie Théorique et Appliquée - AgroParisTech - UNISTRA - Université de Strasbourg - Université de Haute-Alsace (UHA) - Université de Haute-Alsace (UHA) Mulhouse - Colmar - UL - Université de Lorraine - CNRS - Centre National de la Recherche Scientifique - INRAE - Institut National de Recherche pour l’Agriculture, l’Alimentation et l’Environnement)
    Abstract: This paper shows how minimax regret sheds new light on an old economic topic, market-exit games. It focuses on wars of attrition, namely overcrowded duopoly markets where the strategic variable is the exit time. The only symmetric Nash equilibrium (NE) of the game studied is a mixed-strategy equilibrium that leads to a null expected payoff, i.e., the payoff a firm gets when it immediately exits the market. This result is not convincing, both from a behavioral and from a strategic viewpoint. The minimax regret approach that builds upon opposite regrets — exiting the market too late and exiting the market too early — is more convincing and ensures that both firms obtain a strictly positive expected payoff.
    Keywords: War of attrition, Minimax regret, Mixed-strategy Nash equilibrium, Maximin payoff, Overcrowded market
    Date: 2022–12–11
  3. By: Chatterji, Shurojit (School of Economics, Singapore Management University); Kunimoto, Takashi (School of Economics, Singapore Management University); Salles Ramos, Paulo Daniel (School of Economics, Singapore Management University)
    Abstract: A social choice function (SCF) is said to be Nash implementable if there exists a mechanism in which every Nash equilibrium outcome coincides with that specified by the SCF. The main objective of this paper is to assess the impact of considering mixed strategy equilibria in Nash implementation. To do this, we focus on environments with two agents and restrict attention to finite mechanisms. We call a mixed strategy equilibrium “compelling” if its outcome Pareto dominates any pure strategy equilibrium outcome. We show that if the finite environment and the SCF to be implemented jointly satisfy what we call Condition P+M, we construct a finite mechanism which Nash implements the SCF in pure strategies and possesses no compelling mixed strategy equilibria. This means that the mechanism might possess mixed strategy equilibria which are “not” compelling. Our mechanism has several desirable features: transfers can be completely dispensable; only fi-nite mechanisms are considered; integer games are not invoked; and players’ attitudes toward risk do not matter.
    Keywords: Implementation; compelling equilibria; ordinality; mixed strate-gies; Nash equilibrium
    JEL: C72 D78 D82
    Date: 2024–02–01
  4. By: David Lagziel (BGU); Lotem Ikan (BGU)
    Keywords: evolutionary processes; contest theory; non-Bayesian social learning; polarization
    JEL: C72 D62 D72
    Date: 2023
  5. By: Fatima Khanchouche (UFAS1 - Université Ferhat-Abbas Sétif 1 [Sétif]); Samir Sbabou (UNICAEN - Université de Caen Normandie - NU - Normandie Université, CREM - Centre de recherche en économie et management - UNICAEN - Université de Caen Normandie - NU - Normandie Université - UR - Université de Rennes - CNRS - Centre National de la Recherche Scientifique); Hatem Smoui (CEMOI - Centre d'Économie et de Management de l'Océan Indien - UR - Université de La Réunion); Abderrahmane Ziad (UFAS1 - Université Ferhat-Abbas Sétif 1 [Sétif], CREM - Centre de recherche en économie et management - UNICAEN - Université de Caen Normandie - NU - Normandie Université - UR - Université de Rennes - CNRS - Centre National de la Recherche Scientifique)
    Abstract: In this paper, we examine the class of congestion games with player-specific payoff functions introduced by Milchtaich, I. (1996). Focusing on the special case of two resources, we give a short and simple method for identifying all Nash equilibria in pure strategies. We also provide a computation algorithm based on our theoretical analysis.
    Keywords: game theory, Nash equilibria, congestion games, price of anarchy
    Date: 2024
  6. By: Bramoullé, Y.; Ghiglino, C.
    Abstract: We introduce loss aversion into a model of conspicuous consumption in networks. Agents allocate heterogeneous incomes between a conventional good and a status good. They interact over a connected network and compare their status consumption to their neighbors’ average consumption. We find that aversion to lying below the social reference point has a profound impact. If loss aversion is large relative to income heterogeneity, a continuum of conformist Nash equilibria emerges. Agents have the same status consumption, despite differences in incomes and network positions, and the equilibrium is indeterminate. Otherwise, there is a unique Nash equilibrium and status consumption depends on the interplay between network positions and incomes. Our analysis extends to homothetic and heterogeneous preferences.
    Keywords: Conspicuous Consumption, Loss Aversion, Social Networks
    Date: 2024–03–12
  7. By: Aner Sela (BGU)
    Keywords: Elimination games, all-pay contests, simultaneous contests, sequential contests
    JEL: D44 J31 D72 D82
    Date: 2023
  8. By: Mert Kimya
    Abstract: We provide the first axiomatic treatment of two of the most fundamental far-sighted solution concepts. We then extend our analysis to include an axiomatization of the stable set to the extent that it is farsighted. In fi nite abstract games a solution is the largest consistent set if and only if it is maximally supportable and nonempty. In any abstract game a solution is the farsighted stable set if and only if it is minimally supportable, consistent, conversely consistent and nonempty in finite horizon games. We call the stable set that does not suffer from Harsanyi (1974)'s critique of myopia the Harsanyi stable set. In any abstract game a solution is the Harsanyi stable set if and only if it is simply supportable, consistent, weakly conversely consistent and it satisfi es restricted nonemptiness. The axioms of consistency and converse consistency are the adaptations of the frequently used principles of consistency and converse consistency to a farsighted framework. The axioms of maximal supportability, minimal supportability and simple supportability relate to the commonly held expectations that support these solutions as their stationary states.
    Date: 2024–03
  9. By: Xin Yue Ren; Dena Firoozi
    Abstract: In this paper, we address linear-quadratic-Gaussian (LQG) risk-sensitive mean field games (MFGs) with common noise. In this framework agents are exposed to a common noise and aim to minimize an exponential cost functional that reflects their risk sensitivity. We leverage the convex analysis method to derive the optimal strategies of agents in the limit as the number of agents goes to infinity. These strategies yield a Nash equilibrium for the limiting model. The model is then applied to interbank markets, focusing on optimizing lending and borrowing activities to assess systemic and individual bank risks when reserves drop below a critical threshold. We employ Fokker-Planck equations and the first hitting time method to formulate the overall probability of a bank or market default. We observe that the risk-averse behavior of agents reduces the probability of individual defaults and systemic risk, enhancing the resilience of the financial system. Adopting a similar approach based on stochastic Fokker-Planck equations, we further expand our analysis to investigate the conditional probabilities of individual default under specific trajectories of the common market shock.
    Date: 2024–03
  10. By: Dziubiński, M.; Goyal, S.; Zhou, J.
    Abstract: We study a model of conflict with multiple battlefields and the possibility of investments spillovers between the battlefields. Results of conflicts at the individual battlefields are determined by the Tullock contest success function based on efforts assigned to a battlefield as well as efforts spilling over from the neighbouring battlefields. We characterize Nash equilibria of this model and uncover a network invariance result: equilibrium payoffs, equilibrium total expenditure, and equilibrium probabilities of winning individual battlefields are independent of the network of spillovers. We show that the network invariance holds for any contest success function that is homogeneous of degree zero and has the no-tie property. We define a network index that characterizes equilibrium efforts assignments of the players. We show that the index satisfies neighbourhood inclusion and can, therefore, be considered a network centrality.
    Keywords: Conflict, Investments, Models, Networks
    Date: 2024–02–21
  11. By: Daniel (University of Pavia);
    Abstract: Product design is studied in a simple duopoly where firms compete à la Cournot, goods are hedonically differentiated and consumers have preferences defined over characteristics. What we find is that, in equilibrium, firms choose the same product’s design. This results in horizontal product differentiation being minimal.
    Keywords: Hedonic Product Differentiation, Horizontal Differentiation, Product Design, Cournot Competition
    JEL: D43 L13 L20
    Date: 2024–03
  12. By: Valerio Capraro; Roberto Di Paolo; Matjaz Perc; Veronica Pizziol
    Abstract: Understanding human behaviour in decision problems and strategic interactions has wide-ranging applications in economics, psychology, and artificial intelligence. Game theory offers a robust foundation for this understanding, based on the idea that individuals aim to maximize a utility function. However, the exact factors influencing strategy choices remain elusive. While traditional models try to explain human behaviour as a function of the outcomes of available actions, recent experimental research reveals that linguistic content significantly impacts decision-making, thus prompting a paradigm shift from outcome-based to language-based utility functions. This shift is more urgent than ever, given the advancement of generative AI, which has the potential to support humans in making critical decisions through language-based interactions. We propose sentiment analysis as a fundamental tool for this shift and take an initial step by analyzing 61 experimental instructions from the dictator game, an economic game capturing the balance between self-interest and the interest of others, which is at the core of many social interactions. Our meta-analysis shows that sentiment analysis can explain human behaviour beyond economic outcomes. We discuss future research directions. We hope this work sets the stage for a novel game theoretical approach that emphasizes the importance of language in human decisions.
    Date: 2024–03
  13. By: Giebe, Thomas (Department of Economics and Statistics); Gürtler, Oliver (Department of Economics, University of Cologne)
    Abstract: In competitive settings, disparities in player strength are common. It is intuitively unclear whether a stronger player would opt for larger or smaller effort compared to weaker players. Larger effort could leverage their strength, while lower effort might be justified by their higher probability of winning regardless of effort. We analyze contests with three or more players, exploring when stronger players exert larger or lower effort. To rank efforts, it suffices to compare marginal utilities in situations where efforts are equal. Effort ranking depends on differences in hazard rates (which are smaller for stronger players) and reversed hazard rates (which are larger for stronger players). Compared to weaker players, stronger players choose larger effort in winner-takes-all contests and lower effort in loser-gets-nothing contests. Effort rankings can be non-monotonic in contests with several identical prizes, and they depend on the slopes of players’ pdfs in contests with linear prize structure.
    Keywords: contest theory; heterogeneity; player strength
    JEL: C72 D74 D81
    Date: 2024–03–06
  14. By: David Lagziel (BGU); Yevgeny Tsodikovich (Department of Economics, Bar Ilan University)
    Keywords: Sequential Bayesian Games; Guided Equilibrium; Learning
    JEL: C72 D82 D83
    Date: 2023
  15. By: Zhang Xu; Mingsheng Zhang; Wei Zhao
    Abstract: As firms' pricing strategies increasingly rely on algorithms, two concerns have received much attention: algorithmic tacit collusion and price discrimination. This paper investigates the interaction between these two issues through simulations. In each period, a new buyer arrives with independently and identically distributed willingness to pay (WTP), and each firm, observing private signals about WTP, adopts Q-learning algorithms to set prices. We document two novel mechanisms that lead to collusive outcomes. Under asymmetric information, the algorithm with information advantage adopts a Bait-and-Restrained-Exploit strategy, surrendering profits on some signals by setting higher prices, while exploiting limited profits on the remaining signals by setting much lower prices. Under a symmetric information structure, competition on some signals facilitates convergence to supra-competitive prices on the remaining signals. Algorithms tend to collude more on signals with higher expected WTP. Both uncertainty and the lack of correlated signals exacerbate the degree of collusion, thereby reducing both consumer surplus and social welfare. A key implication is that the over-usage of data, both payoff-relevant and non-relevant, by AIs in competitive contexts will reduce the degree of collusion and consequently lead to a decline in industry profits.
    Date: 2024–03
  16. 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
  17. By: Gergely Horvath; Mofei Jia
    Abstract: We study whether competition for social status induces higher effort provision and efficiency when individuals collaborate with their network neighbors. We consider a laboratory experiment in which individuals choose a costly collaborative effort and their network neighbors. They benefit from their neighbors' effort and effort choices of direct neighbors are strategic complements. We introduce two types of social status in a 2x2 factorial design: 1) individuals receive monetary benefits for incoming links representing popularity; 2) they receive feedback on their relative payoff ranking within the group. We find that link benefits induce higher effort provision and strengthen the collaborative ties relative to the Baseline treatment without social status. In contrast, the ranking information induces lower effort as individuals start competing for higher ranking. Overall, we find that social status has no significant impact on the number of links in the network and the efficiency of collaboration in the group.
    Date: 2024–03
  18. By: Choi, S.; Goyal, S.; Guo, F.; Moisan, F.
    Abstract: Social interactions shape individual behaviour and public policy increasingly uses networks to improve effectiveness. It is therefore important to understand if the theoretical predictions on the relation between networks and individual choice are empirically valid. This paper tests a key result in the theory of games on networks: an individual’s action is proportional to their (Bonacich) centrality. Our experiment shows that individual efforts increase in centrality but at a rate of increase that is lower than the theoretical prediction. Moreover, efforts are higher than predicted in some cases and lower than predicted in other cases. These departures from equilibrium have large effects on individual earnings. We propose a model of network based imitation decision rule to explain these deviations.
    JEL: C92 D83 D85 Z13
    Date: 2024–01–16
  19. By: Seungjin Han; Andrew Leal
    Abstract: This paper proposes Competing Mechanism Games Played Through Agent (CMGPTA), an extension of the GPTA (Prat and Rustichini (2003)), where a Principal can offer any arbitrary mechanism that specifies a transfer schedule for each agent conditional on all Agents' messages. We identify the set of equilibrium allocations using deviator-reporting mechanisms (DRMs) on the path and single transfer schedules off the path. We design a lab experiment implementing DRMs. We observe that implemented outcomes are efficient more often than random. A majority of the time, Agents do tell the truth on the identity of a deviating Principal, despite potential gains from (tacit) collusion on false reports. As play progresses, Agents learn to play with their counterparty Agent with the average predicted probability of collusion on false reports across groups increasing from about 9% at the beginning of the experiment to just under 20% by the end. However, group heterogeneity is significant.
    Date: 2024–03
  20. By: Simon Finster; Patrick Loiseau; Simon Mauras; Mathieu Molina; Bary Pradelski
    Abstract: We study how pricing affects the division of surplus among buyers in auctions for multiple units. Our equity objective may be important, e.g., for competition concerns in downstream markets, complementing the long-standing debate on revenue and efficiency. We study a canonical model of auctions for multiple indivisible units with unit demand buyers and valuations with a private and a common component and consider all pricing rules that are a mixture (i.e., a convex combination) of pay-as-bid and uniform pricing. We propose the winners' empirical variance (WEV), the expected empirical variance of surplus among the winners, as a metric for surplus equity. We show that, for a range of private-common value proportions, a strictly interior mix of pay-as-bid and uniform pricing minimizes WEV. From an equity perspective, auctions with a higher private value component benefit from more price discrimination, whereas only auctions with a sufficiently high common value justify a more uniform pricing rule. We provide a criterion under which strictly mixed pricing dominates uniform pricing, a partial ranking of different mixed pricing formats, and bounds on the WEV-minimizing pricing under the assumption of log-concave signal distributions. In numerical experiments, we further illustrate the WEV-minimal pricing as a function of the private-common-value mix.
    Date: 2024–03
  21. By: Aner Sela (BGU)
    Keywords: Two-sided matching, All-pay contests
    JEL: D44 J31 D72 D82
    Date: 2023

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