nep-gth New Economics Papers
on Game Theory
Issue of 2021‒06‒21
twenty papers chosen by
Sylvain Béal
Université de Franche-Comté

  1. Implementation in Large Population Games with Multiple Equilibria By Sarvesh Bandhu; Ratul Lahkar
  2. Strategic information transmission with sender's approval: the single-crossing case By Sémirat, S.; Forges, F.
  3. Characterization of equilibrium existence and purification in general Bayesian games By Wei He; Xiang Sun; Yeneng Sun; Yishu Zeng
  4. Cyclical behavior of evolutionary dynamics in coordination games with changing payoffs By George Loginov
  5. Combinatorial Algorithms for Matching Markets via Nash Bargaining: One-Sided, Two-Sided and Non-Bipartite By Ioannis Panageas; Thorben Tr\"obst; Vijay V. Vazirani
  6. The Value of a Coordination Game By Kets, Willemien; Kager, Wouter; Sandroni, Alvaro
  7. A check for rational inattention By Howard, Greg
  8. $N$-player and Mean-field Games in It\^{o}-diffusion Markets with Competitive or Homophilous Interaction By Ruimeng Hu; Thaleia Zariphopoulou
  9. The Influence of Empirical and Normative Expectations on Cooperation By Felix Kölle; Simone Quercia
  10. Signatured Deep Fictitious Play for Mean Field Games with Common Noise By Ming Min; Ruimeng Hu
  11. Equal division among the few: an experiment about a coalition formation game By Yukihiko Funaki; Emmanuel Sol; Marc Willinger
  12. Bioelectrical brain activity can predict prosocial behavior By Mikhail Kunavin; Tatiana Kozitsina; Mikhail Myagkov; Irina Kozhevnikova; Mikhail Pankov; Ludmila Sokolova
  13. Contrasting effects of information sharing on common-pool resources extraction behavior: experimental findings By Dimitri Dubois; Stefano Farolfi; Phu Nguyen-Van; Juliette Rouchier
  14. A Note on Optimal Fees for Constant Function Market Makers By Robin Fritsch; Roger Wattenhofer
  15. Interactive Communication in Bilateral Trade By Jieming Mao; Renato Paes Leme; Kangning Wang
  16. Electoral Competition with Costly Policy Changes: A Dynamic Perspective By Gersbach, Hans; Jackson, Matthew O.; Muller, Philippe; Tejada, Oriol
  17. The Optimal Length of Political Terms By Gersbach, Hans; Jackson, Matthew O.; Tejada, Oriol
  18. Asymmetric All-Pay Contests with Spillovers By Maria Betto; Matthew W. Thomas
  19. Growth and Welfare Effects of Interventions in Patent Licensing Negotiations By Kishimoto, Shin; Suzuki, Keishun
  20. The impact of targeting technologies and consumer multi-homing on digital platform competition By Evensen, Charlotte Bjørnhaug; Haugen, Atle

  1. By: Sarvesh Bandhu (Indian Institute of Management, Bangalore); Ratul Lahkar (Ashoka University)
    Abstract: Evolutionary implementation is a standard method of implementation in large population games. Such implementation may, however, be ineffective in certain situations. We consider one such situation where strategic complementarities generate multiple Nash equilibria. The planner constructs an externality adjusted game by adding the positive externalities in the game to the original payoffs. However, strategic complementarities render the Pareto inferior Nash equilibrium evolutionarily stable. The society, therefore, fails to converge to the efficient state of the model leading to the failure of evolutionary implementation. We provide a new solution to this problem of implementation in large population games with multiple equilibria using dominant strategy implementation. Our main result is that the efficient state can be implemented in strictly dominant strategy by applying Pigouvian pricing calculated on the basis of the distribution of reported types.
    Keywords: Aggregative games; Potential games; Externalities; Implementation
    Date: 2021–06
  2. By: Sémirat, S.; Forges, F.
    Abstract: We consider a sender-receiver game, in which the sender has finitely many types and the receiver's decision is a real number. We assume that utility functions are concave, single-peaked and single-crossing. After the cheap talk phase, the receiver makes a decision, which requires the sender's approval to be implemented. Otherwise, the sender "exits". At a perfect Bayesian equilibrium without exit, the receiver must maximize his expected utility subject to the participation constraints of all positive probability types. This necessary condition may not hold at the receiver's prior belief, so that a non-revealing equilibrium may fail to exist. Similarly, a fully revealing equilibrium may not exist either due to the sender's incentive compatibility conditions. We propose a constructive algorithm that always achieves a perfect Bayesian equilibrium without exit.
    JEL: C72 D82
    Date: 2021
  3. By: Wei He; Xiang Sun; Yeneng Sun; Yishu Zeng
    Abstract: This paper studies Bayesian games with general action spaces, correlated types and interdependent payoffs. We introduce the condition of ``decomposable coarser payoff-relevant information'', and show that this condition is both sufficient and necessary for the existence of pure-strategy equilibria and purification from behavioral strategies. As a consequence of our purification method, a new existence result on pure-strategy equilibria is also obtained for discontinuous Bayesian games. Illustrative applications of our results to oligopolistic competitions and all-pay auctions are provided.
    Date: 2021–06
  4. By: George Loginov
    Abstract: The paper presents a model of two-speed evolution in which the payoffs in the population game (or, alternatively, the individual preferences) slowly adjust to changes in the aggregate behavior of the population. The model investigates how, for a population of myopic agents with homogeneous preferences, changes in the environment caused by current aggregate behavior may affect future payoffs and hence alter future behavior. The interaction between the agents is based on a symmetric two-strategy game with positive externalities and negative feedback from aggregate behavior to payoffs, so that at every point in time the population has an incentive to coordinate, whereas over time the more popular strategy becomes less appealing. Under the best response dynamics and the logit dynamics with small noise levels the joint trajectories of preferences and behavior converge to closed orbits around the unique steady state, whereas for large noise levels the steady state of the logit dynamics becomes a sink. Under the replicator dynamics the unique steady state of the system is repelling and the trajectories are unbounded unstable spirals.
    Date: 2021–06
  5. By: Ioannis Panageas; Thorben Tr\"obst; Vijay V. Vazirani
    Abstract: This paper is an attempt to deal with the recent realization (Vazirani, Yannakakis 2021) that the Hylland-Zeckhauser mechanism, which has remained a classic in economics for one-sided matching markets, is likely to be highly intractable. HZ uses the power of a pricing mechanism, which has endowed it with nice game-theoretic properties. Hosseini and Vazirani (2021) define a rich collection of Nash-bargaining-based models for one-sided and two-sided matching markets, in both Fisher and Arrow-Debreu settings, together with implementations using available solvers, and very encouraging experimental results. This naturally raises the question of finding efficient combinatorial algorithms for these models. In this paper, we give efficient combinatorial algorithms based on the techniques of multiplicative weights update (MWU) and conditional gradient descent (CGD) for several one-sided and two-sided models defined in HV 2021. Additionally, we define for the first time a Nash-bargaining-based model for non-bipartite matching markets and solve it using CGD. Furthermore, in every case, we study not only the Fisher but also the Arrow-Debreu version; the latter is also called the exchange version. We give natural applications for each model studied. These models inherit the game-theoretic and computational properties of Nash bargaining. We also establish a deep connection between HZ and the Nash-bargaining-based models, thereby confirming that the alternative to HZ proposed in HV 2021 is a principled one.
    Date: 2021–06
  6. By: Kets, Willemien (University of Oxford); Kager, Wouter; Sandroni, Alvaro
    Abstract: The value of a game is the payoff a player can expect (ex ante) from playing the game. Understanding how the value changes with economic primitives is critical for policy design and welfare. However, for games with multiple equilibria, the value is difficult to determine. We therefore develop a new theory of the value of coordination games. The theory delivers testable comparative statics on the value and delivers novel insights relevant to policy design. For example, policies that shift behavior in the desired direction can make everyone worse off, and policies that increase everyone's payoffs can reduce welfare.
    Date: 2021–06–03
  7. By: Howard, Greg
    Abstract: Models of rational inattention allow agents to make mistakes in their actions while assuming they do not make mistakes in attention allocation. I test this assumption by comparing attention’s marginal benefit (better actions) and marginal cost (less time for future decisions) using millions of online chess moves. I cannot reject that skilled players equalize marginal benefit and marginal cost across different time controls. Bad players, when they have little time, under-adjust their attention allocation, leading them to have higher marginal cost. A simple intervention improves players' attention allocation.
    Keywords: rational inattention, deterministic games, cognitive costs
    JEL: C72 D83 D91
    Date: 2021
  8. By: Ruimeng Hu; Thaleia Zariphopoulou
    Abstract: The paper introduces and analyzes $N$-player and common-noise mean-field games in It\^{o}-diffusion environments, in the context of both complete and incomplete financial markets. The players invest in a finite horizon and in a common market by either competitive or homophilous interactions. In both kinds of market environments, the players have individual risk tolerance coefficients. In the incomplete market setting, these risk tolerances are constants (CARA utilities), while in the complete market, they are assumed to be wealth-independent random variables depending, among others, on upcoming market information. For all these distinct models, we derive explicit or closed-form solutions for the optimal policies and optimal wealth processes, as well as for the related game values.
    Date: 2021–06
  9. By: Felix Kölle (University of Cologne, Albertus Magnus Platz, 50923 Cologne, Germany); Simone Quercia (University of Verona ,via Cantarane 24, 37129 Verona, Italy)
    Abstract: In this paper, we investigate the joint influence of empirical and normative expectations on cooperative behavior. We conduct two experimental studies (n = 243) in which we separately elicit (i) behavior in a public goods game and (ii) social norms under the form of normative and empirical expectations. In a situation where individuals can decide conditionally on others' contributions, we find a strong norm of conditional cooperation whereby people find it socially appropriate to match others contribution and believe others to comply with such rule of behavior. In contrast, when there is strategic uncertainty regarding others' behavior, empirical and normative expectations diverge substantially. While individuals believe that contributing fully to the public good is the most appropriate action, they expect others to contribute only half of their resources. This renders normative expectations unpredictive for average behavior and underlines the importance of a close alignment of empirical and normative expectations for the influence of social norms on behavior.
    Keywords: Cooperation, social norms, expectations, public goods, experiment
    JEL: H41 D63 C92
    Date: 2021–06
  10. By: Ming Min; Ruimeng Hu
    Abstract: Existing deep learning methods for solving mean-field games (MFGs) with common noise fix the sampling common noise paths and then solve the corresponding MFGs. This leads to a nested-loop structure with millions of simulations of common noise paths in order to produce accurate solutions, which results in prohibitive computational cost and limits the applications to a large extent. In this paper, based on the rough path theory, we propose a novel single-loop algorithm, named signatured deep fictitious play, by which we can work with the unfixed common noise setup to avoid the nested-loop structure and reduce the computational complexity significantly. The proposed algorithm can accurately capture the effect of common uncertainty changes on mean-field equilibria without further training of neural networks, as previously needed in the existing machine learning algorithms. The efficiency is supported by three applications, including linear-quadratic MFGs, mean-field portfolio game, and mean-field game of optimal consumption and investment. Overall, we provide a new point of view from the rough path theory to solve MFGs with common noise with significantly improved efficiency and an extensive range of applications. In addition, we report the first deep learning work to deal with extended MFGs (a mean-field interaction via both the states and controls) with common noise.
    Date: 2021–06
  11. By: Yukihiko Funaki (Waseda University); Emmanuel Sol (CEE-M - Centre d'Economie de l'Environnement - Montpellier - UMR 5211 - UM - Université de Montpellier - CNRS - Centre National de la Recherche Scientifique - Montpellier SupAgro - Institut national d’études supérieures agronomiques de Montpellier - Institut Agro - Institut national d'enseignement supérieur pour l'agriculture, l'alimentation et l'environnement - INRAE - Institut National de Recherche pour l’Agriculture, l’Alimentation et l’Environnement); Marc Willinger (CEE-M - Centre d'Economie de l'Environnement - Montpellier - UMR 5211 - UM - Université de Montpellier - CNRS - Centre National de la Recherche Scientifique - Montpellier SupAgro - Institut national d’études supérieures agronomiques de Montpellier - Institut Agro - Institut national d'enseignement supérieur pour l'agriculture, l'alimentation et l'environnement - INRAE - Institut National de Recherche pour l’Agriculture, l’Alimentation et l’Environnement)
    Abstract: We study experimentally a three player sequential and symmetric coalition formation game with empty core. In each round a randomly chosen proposer must choose between a two players coalition or a three players coalition and decide about the payoff division among the coalition members. Players who receive a proposition can accept or reject it. In case of acceptance the game ends. If it is rejected, a new proposer is randomly selected. The game was played repeatedly, with randomly rematched groups. We observe that over 86% of the realized coalitions are two-players coalitions. Three players coalitions are often observed in early rounds but are frequently rejected. Equal splits are the most frequently observed divisions among coalition members, and their frequency increases sharply over time. We propose an extension of von Neumann and Morgenstern (1944)'s notion of stable set to account for our results.
    Date: 2021–05–17
  12. By: Mikhail Kunavin (Babkina); Tatiana Kozitsina (Babkina); Mikhail Myagkov; Irina Kozhevnikova; Mikhail Pankov; Ludmila Sokolova
    Abstract: Generally, people behave in social dilemmas such as proself and prosocial. However, inside social groups, people have a tendency to choose prosocial alternatives due to in-group favoritism. The bioelectrical activity of the human brain shows the differences between proself and prosocial exist even out of a socialized group. Moreover, a group socialization strengthens these differences. We used EEG System, "Neuron-Spectrum-4/EPM" (16 channels), to track the brain bioelectrical activity during decision making in laboratory experiments with the Prisoner's dilemma game and the short-term socialization stage. We compared the spatial distribution of the spectral density during the different experimental parts. The noncooperative decision was characterized by the increased values of spectral the beta rhythm in the orbital regions of prefrontal cortex. The cooperative choice, on the contrary, was accompanied by the theta-rhythm activation in the central cortex regions in both hemispheres and the high-frequency alpha rhythm in the medial regions of the prefrontal cortex. People who increased the cooperation level after the socialization stage was initially different from the ones who decreased the cooperation in terms of the bioelectrical activity. Well-socialized participants differed by increased values of spectral density of theta-diapason and decreased values of spectral density of beta-diapason in the middle part of frontal lobe. People who decreased the cooperation level after the socialization stage was characterized by decreased values of spectral density of alpha rhythm in the middle and posterior convex regions of both hemispheres.
    Date: 2021–05
  13. By: Dimitri Dubois (CEE-M - Centre d'Economie de l'Environnement - Montpellier - UMR 5211 - UM - Université de Montpellier - CNRS - Centre National de la Recherche Scientifique - Montpellier SupAgro - Institut national d’études supérieures agronomiques de Montpellier - Institut Agro - Institut national d'enseignement supérieur pour l'agriculture, l'alimentation et l'environnement - INRAE - Institut National de Recherche pour l’Agriculture, l’Alimentation et l’Environnement); Stefano Farolfi (UMR G-EAU - Gestion de l'Eau, Acteurs, Usages - Cirad - Centre de Coopération Internationale en Recherche Agronomique pour le Développement - IRD - Institut de Recherche pour le Développement - AgroParisTech - Montpellier SupAgro - Institut national d’études supérieures agronomiques de Montpellier - Institut Agro - Institut national d'enseignement supérieur pour l'agriculture, l'alimentation et l'environnement - INRAE - Institut National de Recherche pour l’Agriculture, l’Alimentation et l’Environnement, Cirad-ES - Département Environnements et Sociétés - Cirad - Centre de Coopération Internationale en Recherche Agronomique pour le Développement); Phu Nguyen-Van (BETA - Bureau d'Économie Théorique et Appliquée - UL - Université de Lorraine - UNISTRA - Université de Strasbourg - CNRS - Centre National de la Recherche Scientifique - INRAE - Institut National de Recherche pour l’Agriculture, l’Alimentation et l’Environnement); Juliette Rouchier (LAMSADE - Laboratoire d'analyse et modélisation de systèmes pour l'aide à la décision - Université Paris Dauphine-PSL - PSL - Université Paris sciences et lettres - CNRS - Centre National de la Recherche Scientifique)
    Abstract: This paper experimentally investigates the impact of different information sharing mechanisms in a common-pool resource game, with a view to finding a mechanism that is both efficient and inexpensive for the managing agency. More precisely, we compare the observed extraction levels produced as a result of three mechanisms: a mandatory information sharing mechanism and two voluntary information sharing mechanisms that differ in the degree of freedom given to the players. Our main result is that a voluntary information sharing mechanism could help in reaching a lower average extraction level than that observed with the mandatory mechanism.
    Date: 2020–11–01
  14. By: Robin Fritsch; Roger Wattenhofer
    Abstract: We suggest a framework to determine optimal trading fees for constant function market makers (CFMMs) in order to maximize liquidity provider returns. In a setting of multiple competing liquidity pools, we show that no race to the bottom occurs, but instead pure Nash equilibria of optimal fees exist. We theoretically prove the existence of these equilibria for pools using the constant product trade function used in popular CFMMs like Uniswap. We also numerically compute the equilibria for a number of examples and discuss the effects the equilibrium fees have on capital allocation among pools. Finally, we use our framework to compute optimal fees for real world pools using past trade data.
    Date: 2021–05
  15. By: Jieming Mao; Renato Paes Leme; Kangning Wang
    Abstract: We define a model of interactive communication where two agents with private types can exchange information before a game is played. The model contains Bayesian persuasion as a special case of a one-round communication protocol. We define message complexity corresponding to the minimum number of interactive rounds necessary to achieve the best possible outcome. Our main result is that for bilateral trade, agents don't stop talking until they reach an efficient outcome: Either agents achieve an efficient allocation in finitely many rounds of communication; or the optimal communication protocol has infinite number of rounds. We show an important class of bilateral trade settings where efficient allocation is achievable with a small number of rounds of communication.
    Date: 2021–06
  16. By: Gersbach, Hans; Jackson, Matthew O.; Muller, Philippe; Tejada, Oriol
    Abstract: We analyze dynamic electoral competition policy changes. The costs of changing a policy increase with the extent of the shift and generate an incumbency advantage. We characterize the dynamics of Markov equilibria in terms of history and party polarization, and analyze how policies are influenced by the amplitude and convexity of costs of change, as well as by the degree of party and voter farsightedness. Regardless of the initial policy, party choices converge in the long run to a stochastic alternation between two (regions of) policies, with transitions occurring when office-holders suffer a shock to their capacity or valence. Although costs of change have a moderating effect on policies, full convergence to the median voter position does not take place.
    Keywords: costs of change; democracy; dynamic elections; Markov perfect equilibrium; Political Polarization
    JEL: C72 C73 D72 D78
    Date: 2020–06
  17. By: Gersbach, Hans; Jackson, Matthew O.; Tejada, Oriol
    Abstract: We analyze the optimal length of political terms (equivalently, the optimal frequency with which elections should be held) when the candidates of two polarized parties compete for office and the median voter shifts over time. Office-holders determine policy and experience persistent random shocks to their valence. Policy changes are costly for citizens and politicians. Optimal term-length balances the frequency of costly policy changes when parties change office with the incumbent's average valence during tenure. We find that optimal term-length increases with party polarization, with the degree to which the median voter cares about valence, and with the frequency and the size of swings in the electorate. In contrast, optimal term-length decreases when candidates for office undergo less scrutiny or when parties care more about future outcomes. Finally, with small swings in the electorate and large polarization, optimal term-length increases if checks and balances increase.
    Keywords: costs of change; Elections; Polarization; term-length
    JEL: C72 C73 D72 D78
    Date: 2020–06
  18. By: Maria Betto; Matthew W. Thomas
    Abstract: When opposing parties compete for a prize, the sunk effort players exert during the conflict can affect the value of the winner's reward. These spillovers can have substantial influence on the equilibrium behavior of participants in applications such as lobbying, warfare, labor tournaments, marketing, and R&D races. To understand this influence, we study a general class of asymmetric, two-player all-pay contests where we allow for spillovers in each player's reward. The link between participants' efforts and rewards yields novel effects -- in particular, players with higher costs and lower values than their opponent sometimes extract larger payoffs.
    Date: 2021–06
  19. By: Kishimoto, Shin; Suzuki, Keishun
    Abstract: Policy makers sometimes intervene in patent licensing negotiations to guide licensing fees, but the impacts of such interventions on economic growth and welfare are relatively unknown. This paper develops a novel Schumpeterian growth model featuring a cooperative game-theoretic framework that describes negotiations about licensing fees. We find that the growth effect of intervention is negative if firms can raise unlimited external funds for their R&D investment. However, when the amount of external funds available is limited, both the growth and the welfare effects of intervention can be positive. This result means that interventions are desirable when the internal funds of firms are the main source of their R&D investment.
    Keywords: Patent licensing negotiations, Schumpeterian growth, Cooperative game, Patent protection, Financial constraints.
    JEL: C71 D45 O30
    Date: 2021–05–28
  20. By: Evensen, Charlotte Bjørnhaug (Dept. of Economics, Norwegian School of Economics and Business Administration); Haugen, Atle (Dept. of Economics, Norwegian School of Economics and Business Administration)
    Abstract: Abstract In this paper, we address how targeting and consumer multi-homing impact platform competition and market equilibria in two-sided markets. We analyze platforms that are financed by both advertising and subscription fees, and let them adopt a targeting technology with increasing performance in audience size: a larger audience generates more consumer data, which improves the platforms’ targeting ability and allows them to extract more ad revenues. Targeting therefore increases the importance of attracting consumers. Previous literature has shown that this could result in fierce price competition if consumers subscribe to only one platform (i.e. single-home). Surprisingly, we find that pure single-homing possibly does not constitute a Nash equilibrium. Instead, platforms might rationally set prices that induce consumers to subscribe to more than one platform (i.e. multi-home). With multi-homing, a platform’s audience size is not restricted by the number of subscribers on rival platforms. Hence, multi-homing softens the competition over consumers. We show that this might imply that equilibrium profit is higher with than without targeting, in sharp contrast to what previous literature predicts.
    Keywords: Two-sided markets; digital platforms; targeted advertising; incremental pricing; consumer multi-homing.
    JEL: D11 D21 L13 L82
    Date: 2021–06–10

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