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on Game Theory |
| By: | Francisco Cabo (UVa - Universidad de Valladolid [Valladolid]); Alain Jean-Marie (NEO - Network Engineering and Operations - CRISAM - Inria Sophia Antipolis - Méditerranée - Inria - Institut National de Recherche en Informatique et en Automatique, CRISAM - Inria Sophia Antipolis - Méditerranée - Inria - Institut National de Recherche en Informatique et en Automatique); Mabel Tidball (CEE-M - Centre d'Economie de l'Environnement - Montpellier - CNRS - Centre National de la Recherche Scientifique - INRAE - Institut National de Recherche pour l’Agriculture, l’Alimentation et l’Environnement - Institut Agro Montpellier - Institut Agro - Institut national d'enseignement supérieur pour l'agriculture, l'alimentation et l'environnement - UM - Université de Montpellier) |
| Abstract: | Social context gives rise, in some individuals, to a desire to conform with other people. Conversely, other people desire to be exclusive or different from the "common herd". We study the interaction between two different agents: the positional player, characterized by the snob effect, and the conformist player, characterized by the bandwagon effect. Both agents engage in a public good game. For a static game we prove that some contribution is feasible only if the status concern of the positional player is sufficiently large. Moreover, contribution by both players requires also that the conformist player sees private contributions as complements. We also analyze how status concerns influence social welfare. In the second part of the paper, we extent the game to a dynamic setting, considering individuals who are change-adverse and who compare their current action against the opponent's past action. Convergence to the static Nash equilibrium can be monotone, oscillating, or spiral. Numerical simulations show that some properties of contributions and utilities along the transition path can be different than those in the long run; specifically, non-monotone convergence can induce overshooting in contributions allowing for over/undershooting in welfare. |
| Keywords: | Public good, positional concerns, inertia, static and dynamic game. |
| Date: | 2023–06–30 |
| URL: | http://d.repec.org/n?u=RePEc:hal:wpaper:hal-04147447&r=gth |
| By: | Eduardo Abi Jaber (X - École polytechnique); Eyal Neuman (Imperial College London); Moritz Voss (UCLA Vision Lab - UCLA - University of California [Los Angeles] - UC - University of California) |
| Abstract: | We consider a general class of nite-player stochastic games with mean-eld interaction, in which the linear-quadratic cost functional includes linear operators acting on controls in L2. We propose a novel approach for deriving the Nash equilibrium of the game explicitly in terms of operator resolvents, by reducing the associated rst order conditions to a system of stochastic Fredholm equations of the second kind and deriving their closed form solution. Furthermore, by proving stability results for the system of stochastic Fredholm equations we derive the convergence of the equilibrium of the N-player game to the corresponding mean-eld equilibrium. As a by-product we also derive an ε-Nash equilibrium for the mean-eld game, which is valuable in this setting as we show that the conditions for existence of an equilibrium in the meaneld limit are less restrictive than in the nite-player game. Finally we apply our general framework to solve various examples, such as stochastic Volterra linear-quadratic games, models of systemic risk and advertising with delay, and optimal liquidation games with transient price impact. |
| Keywords: | mean-field games, Nash equilibrium, Volterra stochastic control, optimal portfolio liquidation, systemic risk, price impact |
| Date: | 2023–06–06 |
| URL: | http://d.repec.org/n?u=RePEc:hal:wpaper:hal-04119787&r=gth |
| By: | Noelia Juarez (UNSL/CONICET); Paola B. Manasero (UNSL/CONICET); Oviedo Jorge (UNSL/CONICET) |
| Abstract: | In a many-to-one matching market with substitutable preferences, we analyze the game induced by a stable rule. When both sides of the market play strategically, we show that any stable rule implements, in Nash equilibrium, the individually rational matchings. Also, when only workers play strategically and firms’ preferences satisfy the law of aggregated demand, we show that any stable rule implements, in Nash equilibrium, the stable matchings |
| Keywords: | Stable matchings, Nash equilibrium, substitutable preferences, matching game |
| JEL: | C78 D47 |
| Date: | 2023–07 |
| URL: | http://d.repec.org/n?u=RePEc:aoz:wpaper:255&r=gth |
| By: | Louis Abraham (UP1 - Université Paris 1 Panthéon-Sorbonne, PRISM Sorbonne - Pôle de recherche interdisciplinaire en sciences du management - UP1 - Université Paris 1 Panthéon-Sorbonne) |
| Abstract: | In this study, we present models where participants strategically select their risk levels and earn corresponding rewards, mirroring real-world competition across various sectors. Our analysis starts with a normal form game involving two players in a continuous action space, confirming the existence and uniqueness of a Nash equilibrium and providing an analytical solution. We then extend this analysis to multi-player scenarios, introducing a new numerical algorithm for its calculation. A key novelty of our work lies in using regret minimization algorithms to solve continuous games through discretization. This groundbreaking approach enables us to incorporate additional real-world factors like market frictions and risk correlations among firms. We also experimentally validate that the Nash equilibrium in our model also serves as a correlated equilibrium. Our findings illuminate how market frictions and risk correlations affect strategic risk-taking. We also explore how policy measures can impact risk-taking and its associated rewards, with our model providing broader applicability than the Diamond-Dybvig framework. We make our methodology and code open-source 1. Finally, we contribute methodologically by advocating the use of algorithms in economics, shifting focus from finite games to games with continuous action sets. Our study provides a solid framework for analyzing strategic interactions in continuous action games, emphasizing the importance of market frictions, risk correlations, and policy measures in strategic risk-taking dynamics. |
| Date: | 2023–05–31 |
| URL: | http://d.repec.org/n?u=RePEc:hal:wpaper:hal-04112160&r=gth |
| By: | Frédéric Koessler (HEC Paris - Ecole des Hautes Etudes Commerciales, GREGHEC - Groupement de Recherche et d'Etudes en Gestion - HEC Paris - Ecole des Hautes Etudes Commerciales - CNRS - Centre National de la Recherche Scientifique); Marieke Pahlke (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, 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 des Ponts ParisTech - CNRS - Centre National de la Recherche Scientifique - INRAE - Institut National de Recherche pour l’Agriculture, l’Alimentation et l’Environnement) |
| Abstract: | We use a notion of maxmin self-confirming equilibrium (MSCE) to study the optimal design of players' feedbacks about others' behavior in games with ambiguity averse players. Coarse feedbacks shape strategic uncertainty and can therefore modify players' equilibrium strategies in an advantageous way. We characterize MSCE and study the equilibrium implications of coarse feedbacks in various classes of games. We show how feedbacks should be optimally designed to improve contributions in generalized volunteer dilemmas and public good games with strategic substitutes, strategic complements, or more general production functions. We also study games with negative externalities and strategic substitutes such as Cournot oligopolies. In general, perfect and no feedbacks are suboptimal. Some results are extended to α-maxmin preferences. |
| Keywords: | Self-confirming equilibrium, Ambiguity aversion, Information feedback, Strategic uncertainty, Public good games, Volunteer dilemma |
| Date: | 2023–03 |
| URL: | http://d.repec.org/n?u=RePEc:hal:wpaper:halshs-04039083&r=gth |
| By: | Felix Kölle (Univeristy of Cologne); Simone Quercia (University of Verona); Egon Tripodi (Hertie School) |
| Abstract: | Social interactions predominantly take place under the shadow of the future. Previous literature explains cooperation in indefinitely repeated prisoner’s dilemma as predominantly driven by self-interested strategic considerations. This paper provides a causal test of the importance of social preferences for cooperation, varying the composition of interactions to be either homogeneous or heterogeneous in terms of these preferences. Through a series of pre-registered experiments (N = 1, 074), we show that groups of prosocial individuals achieve substantially higher levels of cooperation. The cooperation gap between prosocial and selfish groups persists even when the shadow of the future is increased to make cooperation attractive for the selfish and when common knowledge about group composition is removed. |
| Keywords: | cooperation; indefinitely repeated games; prisoner’s dilemma; social preferences; experiment; |
| JEL: | C73 C91 C92 |
| Date: | 2023–06–30 |
| URL: | http://d.repec.org/n?u=RePEc:rco:dpaper:406&r=gth |
| By: | J. Atsu Amegashie |
| Abstract: | I consider a market with two firms, a minority group of customers, and a bigoted (racist, ethnocentric, xenophobic, or sexist) majority group of customers. There exists a Nash equilibrium with full segregation in which a low-price firm serves only the minority and a high-price firm serves only the majority. There is also a partial-integration equilibrium in which a high-price firm serves only the majority while a low-price firm serves both the minority and majority. Paradoxically, if the minority group is sufficiently big and the majority is sufficiently prejudiced, then both equilibria hold in the sense that the high-price firm does not lose customers, although its competitor charges a lower price. If the firms can price discriminate, none of these equilibria will hold. The partial integration equilibrium depends on how the prejudice of the majority is modelled. |
| Keywords: | customer discrimination, majority, markets, minority, segregation |
| JEL: | J15 |
| Date: | 2023 |
| URL: | http://d.repec.org/n?u=RePEc:ces:ceswps:_10453&r=gth |
| By: | Rafiq Friperson (Vrije Universiteit Amsterdam); Hessel Oosterbeek (University of Amsterdam); Bas van der Klaauw (Vrije Universiteit Amsterdam) |
| Abstract: | Sellers in real-estate markets, on internet platforms, in auction houses, and so forth, routinely pose non-binding price requests. Using a laboratory experiment, we examine how competition moderates the way such cheap-talk communication affects trade between buyers and sellers. For bilateral trade, the literature has identified efficiency, anchoring, and granularity effects of cheap-talk communication on negotiation outcomes. Our results show that most of these effects survive with competition, although some of them become weaker. Our main findings are the following: (i) The ability of sellers to make non-binding price requests has a positive effect on efficiency in that it helps trading partners close marginal deals both in bilateral bargaining and in competition; (ii) Competition reduces the informativeness of the price requests and weakens the anchoring effect of the level of the price request; (iii) Sellers communicating more granular price requests attract more granular buyer bids; (iv) The granularity of the seller’s price request does not impact the selling price. |
| Keywords: | Cheap-talk communication, efficiency, anchoring, price granulatiry, laboratory experiment |
| JEL: | C72 C92 D91 |
| Date: | 2023–06–22 |
| URL: | http://d.repec.org/n?u=RePEc:tin:wpaper:20230035&r=gth |
| By: | Shiri Alon (Department of Economics, Bar-Ilan University); Sarah Auster (Department of Economics, University of Bonn); Gabi Gayer (Department of Economics, Bar-Ilan University); Stefania Minardi (Department of Economics and Decision Sciences, HEC Paris) |
| Abstract: | A strategic sender collects data with the goal of persuading a receiver to adopt a new action. The receiver assesses the profitability of adopting the action by following a classical statistics approach: she forms an estimate via the similarity-weighted empirical frequencies of outcomes in past cases, sharing some attributes with the problem at hand. The sender has control over the characteristics of the sampled cases and discloses the outcomes of his study truthfully. We characterize the sender's optimal sampling strategy as the outcome of a greedy algorithm. The sender provides more relevant data---consisting of observations sharing relatively more characteristics with the current problem---when the sampling capacity is low, when a large amount of initial public data is available, and when the estimated benefit of adoption according to this public data is low. Competition between senders curbs incentives for biasing the receiver's estimate and leads to more balanced datasets. |
| Keywords: | Persuasion, case-based inference, similarity-weighted frequencies |
| JEL: | D81 D83 |
| Date: | 2023–07 |
| URL: | http://d.repec.org/n?u=RePEc:ajk:ajkdps:245&r=gth |
| By: | Jibang Wu; Haifeng Xu; Yifan Guo; Weijie Su |
| Abstract: | This paper extends the Isotonic Mechanism from the single-owner to multi-owner settings, in an effort to make it applicable to peer review where a paper often has multiple authors. Our approach starts by partitioning all submissions of a machine learning conference into disjoint blocks, each of which shares a common set of co-authors. We then employ the Isotonic Mechanism to elicit a ranking of the submissions from each author and to produce adjusted review scores that align with both the reported ranking and the original review scores. The generalized mechanism uses a weighted average of the adjusted scores on each block. We show that, under certain conditions, truth-telling by all authors is a Nash equilibrium for any valid partition of the overlapping ownership sets. However, we demonstrate that while the mechanism's performance in terms of estimation accuracy depends on the partition structure, optimizing this structure is computationally intractable in general. We develop a nearly linear-time greedy algorithm that provably finds a performant partition with appealing robust approximation guarantees. Extensive experiments on both synthetic data and real-world conference review data demonstrate the effectiveness of this generalized Isotonic Mechanism. |
| Date: | 2023–06 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2306.11154&r=gth |
| By: | Kwonhyung Lee; Yejin Lim; Sunghyun Cho |
| Abstract: | Migrant laborers subject to ROK's Employment Permit System(EPS) must strike a balance between host country's high wage and 'Depreciation of skill-relevance entailed by immigration', whilst taking account of the 'migration costs'. This study modelizes the optimization mechanism of migrant workers and the firms hiring them -- then induces the solution of the very model, namely, 'Subgame Perfect Nash Equilibrium(SPNE)', by utilizing game theory's 'backward induction' method. Analyzing the dynamics between variables at SPNE state, the attained stylized facts are what as follows; [1]Host nation's skill-relevance and wage differential have positive correlation. [2]Emigrating nation's skill-relevance and wage differential have negative correlation. Both stylized facts -- [1, 2] -- are operationalized into 'Host nation skill-relevance hypothesis(H1)' and 'Emigrating nation skill-relevance hypothesis(H2)', respectively; of which are thoroughly tested by OLS linear regression analysis. In all sex/gender parameters(Total/Men/Women), test results support both hypotheses with statistical significance, thereby inductively substantiating the constructed model. This paper contributes to existing labor immigration literature in three following aspects: (1)Stimulate the economic approach to migrant labor analysis, and by such means, break away from the overflow of sociology, anthropology, political science, and jurisprudence in prior studies; (2)Shed a light on the EPS's microeconomic interaction process, of which was left undisclosed as a 'black box'; (3)Seek a complementary synthesis of two grand strands of research methodology -- that is, deductive modeling and inductive statistics. |
| Date: | 2023–06 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2306.08829&r=gth |
| By: | Khan, Abhimanyu; Peeters, Ronald |
| Abstract: | We develop a framework to analyse stability of cartels in differentiated Cournot oligopolies when multiple cartels may exist in the market. The consideration of formation of multiple cartels is in direct contrast to the existing literature which assumes, without further justification, that at most a single cartel may be formed, and we show that this consideration has markedly different implications for cartel stability. We define a cartel configuration to be stable if: (i) a firm in a cartel does not find it more profitable to leave the cartel and operate independently, (ii) a firm that operates independently does not find it more profitable to join an existing cartel, (iii) a firm in a cartel does not find it more profitable to join another existing cartel or form a new cartel with an independent firm, and (iv) two independent firms do not find it more profitable to form a new cartel. We show that now, when multiple cartels may exist in the market, a single cartel is never stable. |
| Keywords: | multiple cartels; stability; differentiated market. |
| JEL: | C70 D43 L13 |
| Date: | 2023–06–26 |
| URL: | http://d.repec.org/n?u=RePEc:pra:mprapa:117766&r=gth |
| By: | Rey, Patrick; Iossa, Elisabetta; Loertscher, Simon; Leslie M. Marx, |
| Abstract: | While antitrust authorities strive to detect, prosecute, and thereby deter collusive conduct, entities harmed by that conduct are also advised to pursue their own strategies to deter collusion. The implications of such delegation of deterrence have largely been ignored, however. In a procurement context, we find that buyers may prefer to accommodate rather than deter collusion among their suppliers. We also show that a multi-market buyer, such as a centralized procurement authority, may optimally deter collusion when multiple independent buyers would not, consistent with the view that “large” buyers are less susceptible to collusion. |
| Keywords: | Collusion; Cartel; Auction; Procurement; Reserves; Sustainability and initiation of collusion; Coordinated effects |
| JEL: | D44 D82 H57 L41 |
| Date: | 2023–06–05 |
| URL: | http://d.repec.org/n?u=RePEc:tse:wpaper:128130&r=gth |
| By: | Matthew Knowles (University of Cologne); Mario Lupoli (University of St Andrews) |
| Abstract: | We develop a new measure of wage rigidity, the Nash wage elasticity (NWE). The NWE is the percentage change in the actual wage rate when the wage that would occur under Nash bargaining changes by 1%. We show that the NWE can be measured from aggregate data under relatively weak assumptions which hold across a large class of search and matching models. The empirical value can then be compared with the values predicted by specific models in this class. In the US data, our estimates of the NWE are generally between 0 and 0.1, indicating that, for both continuing workers and new hires, (a) there is a high degree of wage rigidity and (b) Nash bargaining provides a poor description of wage setting. We show that our estimates imply that wage rigidity greatly amplifies business cycles: A simple SAM model suggests that, if workers were paid Nash-bargained wages rather than actual wages, then the cyclical volatility of unemployment would decrease to less than one seventh of what it is in the data. We compare our results to various models of rigid and flexible wages in the literature. |
| Keywords: | Business Cycles; Unemployment; Wage Rigidity; Nash Bargaining |
| JEL: | E32 J30 |
| Date: | 2023–06 |
| URL: | http://d.repec.org/n?u=RePEc:ajk:ajkdps:240&r=gth |
| By: | Theresa Hager (Institute for Comprehensive Analysis of the Economy, Johannes Kepler University Linz, Austria); Patrick Mellacher (Schumpeter Centre, University of Graz, Austria); Magdalena Rath (Schumpeter Centre, University of Graz, Austria) |
| Abstract: | We study the impact of gender norms on the distribution of paid and unpaid labor between women and men in an intra-household bargaining model featuring endogenous social norms. In contrast to the previous literature, which assumes a homogeneous social norm, agents are connected via explicitly modeled social networks and accordingly face heterogeneous perceptions of gender norms. In our model, social pressure to conform to gender norms exacerbates gender inequalities in the distribution of paid and unpaid labor that may result from a gender pay gap or gender-specific preferences. However, we show that the behavior of agents connected in different standardized social networks is significantly closer to a situation in which agents face no social pressure than in a scenario in which the whole of society perceives homogeneous gender norms. This is particularly true if agents are more likely to form connections to other agents that have similar preferences. |
| Date: | 2023–06 |
| URL: | http://d.repec.org/n?u=RePEc:ico:wpaper:147&r=gth |
| By: | Otsu, Taisuke; Pesendorfer, Martin; Sasaki, Yuya; Takahashi, Yuya |
| Abstract: | We propose a multiplicity-robust estimation method for static or dynamic games. The method allows for distinct behaviors and strategies across markets by treating market-specific behaviors as correlated latent variables, with their conditional probability measure treated as an infinite-dimensional nuisance parameter. Instead of solving the intermediate infinite-dimensional optimization problem, we consider the equivalent finite-dimensional dual problem. This property allows for a practically feasible characterization of the identified region for the structural parameters. We apply the estimation method to newspaper market previously studied in Gentzkow et al. (American Economic Review 104 (2014), 3073–114) to characterize the identified region of marginal costs. |
| JEL: | J1 |
| Date: | 2022–08–01 |
| URL: | http://d.repec.org/n?u=RePEc:ehl:lserod:112785&r=gth |