nep-gth New Economics Papers
on Game Theory
Issue of 2023‒05‒22
twenty-one papers chosen by
Sylvain Béal
Université de Franche-Comté

  1. Equilibrium-Invariant Embedding, Metric Space, and Fundamental Set of $2\times2$ Normal-Form Games By Luke Marris; Ian Gemp; Georgios Piliouras
  2. Coordination on networks with farsighted and myopic agents By Ana Mauleon; Simon Schopohl; Akylai Taalaibekova; Vincent Vannetelbosch
  3. Affective Interdependence and Welfare By Aviad Heifetz; Enrico Minelli; Herakles Polemarchakis
  4. Time-Inconsistency in Linear Quadratic Stochastic Differential Games By Ali Lazrak; Hanxiao Wang; Jiongmin Yong
  5. Communication in the Infinitely Repeated Prisoner's Dilemma: Theory and Experiments By Maximilian Andres
  6. Characterizing the Nash bargaining solution with continuity and almost no individual rationality By NAKAMURA, Kensei
  7. Cooperation and ethical choices through an experimental approach By Ngoc Thao NOET; Serge Blondel
  8. Partition-based Stability of Coalitional Games By Jian Yang
  9. Pure-Strategy Equilibrium in the Generalized First-Price Auction By Ostrovsky, Michael; Skrzypacz, Andy
  10. A Partial Order for Strictly Positive Coalitional Games and a Link from Risk Aversion to Cooperation By Jian Yang
  11. Covert learning and disclosure By Matteo Escud\'e
  12. The Evolution of Ostracism in Human Societies By Noblit, Graham Alexander; Henrich, Joseph
  13. Network Effects on Information Acquisition by DeGroot Updaters By Miguel Risco
  14. Normative Conflict and Normative Change By Noblit, Graham Alexander; Hadfield, Gillian
  15. Bargaining-equilibrium equivalence By Bhowmik, Anuj; Saha, Sandipan
  16. Persuasive Lobbying and the Value of Connections By Awad, Emiel; Minaudier, Clement
  17. A Unified Theory of Value: Oligopolistic Competition and Optimum Product Diversity By Cordoba, Juan Carlos; Liu, Xiying
  18. Optimal Delegation and Information Transmission under Limited Awareness By Sarah Auster; Nicola Pavoni
  19. Bargaining Theory and the Copyright Royalty Board’s Rate Setting Mandate for Interactive Streaming of Music By Elliott Hughes; Richard Watt
  20. Persuading a Wishful Thinker By Victor Augias; Daniel M A Barreto
  21. Data Tracking under Competition By Bimpikis, Kostas; Morgenstern, Ilan; Saban, Daniela

  1. By: Luke Marris; Ian Gemp; Georgios Piliouras
    Abstract: Equilibrium solution concepts of normal-form games, such as Nash equilibria, correlated equilibria, and coarse correlated equilibria, describe the joint strategy profiles from which no player has incentive to unilaterally deviate. They are widely studied in game theory, economics, and multiagent systems. Equilibrium concepts are invariant under certain transforms of the payoffs. We define an equilibrium-inspired distance metric for the space of all normal-form games and uncover a distance-preserving equilibrium-invariant embedding. Furthermore, we propose an additional transform which defines a better-response-invariant distance metric and embedding. To demonstrate these metric spaces we study $2\times2$ games. The equilibrium-invariant embedding of $2\times2$ games has an efficient two variable parameterization (a reduction from eight), where each variable geometrically describes an angle on a unit circle. Interesting properties can be spatially inferred from the embedding, including: equilibrium support, cycles, competition, coordination, distances, best-responses, and symmetries. The best-response-invariant embedding of $2\times2$ games, after considering symmetries, rediscovers a set of 15 games, and their respective equivalence classes. We propose that this set of game classes is fundamental and captures all possible interesting strategic interactions in $2\times2$ games. We introduce a directed graph representation and name for each class. Finally, we leverage the tools developed for $2\times2$ games to develop game theoretic visualizations of large normal-form and extensive-form games that aim to fingerprint the strategic interactions that occur within.
    Date: 2023–04
  2. By: Ana Mauleon (CORE - Center of Operation Research and Econometrics [Louvain] - UCL - Université Catholique de Louvain = Catholic University of Louvain); Simon Schopohl (CORE - Center of Operation Research and Econometrics [Louvain] - UCL - Université Catholique de Louvain = Catholic University of Louvain); Akylai Taalaibekova (CES - Centre d'économie de la Sorbonne - UP1 - Université Paris 1 Panthéon-Sorbonne - CNRS - Centre National de la Recherche Scientifique); Vincent Vannetelbosch (CORE - Center of Operation Research and Econometrics [Louvain] - UCL - Université Catholique de Louvain = Catholic University of Louvain)
    Abstract: We study a coordination game on a fixed connected network where players have to choose between two projects. Some players are moderate (i.e. they are ex-ante indifferent between both projects) while others are stubborn (i.e. they always choose the same project). Benefits for moderate players are increasing in the number of neighbors who choose the same project. In addition, players are either farsighted or myopic. Farsighted players anticipate the reactions of others while myopic players do not. We show that, when all players are farsighted, full coordination among the moderate players is reached except if there are stubborn players for both projects. When the population is mixed, the set of stable strategy profiles is a refinement of the set of Nash equilibrium strategy profiles. In fact, turning myopic players into farsighted ones eliminates gradually the inefficient Nash equilibria. Finally, we consider a social planner who can improve coordination by means of two policy instruments: adding links to the network (socialization) and/or turning myopic players into farsighted ones (education).
    Keywords: Networks, Coordination problems, Stubborn players, Farsighted players, Stability
    Date: 2022
  3. By: Aviad Heifetz (The Open University of Israel); Enrico Minelli (University of Brescia); Herakles Polemarchakis (University of Warwick)
    Abstract: Purely affective interaction allows the welfare of an individual to depend on her own actions and on the profile of welfare levels of others. Under an assumption on the structure of mutual affection that we interpret as Ònon- explosive mutual affection, Ó we show that equilibria of simultaneous-move affective interaction are Pareto optimal independently of whether or not an induced standard game exists. Moreover, if purely affective interaction induces a standard game, then an equilibrium profile of actions is a Nash equilibrium of the game, and this Nash equilibrium and Pareto optimal profile of strategies is locally dominant.
    Date: 2023–04
  4. By: Ali Lazrak; Hanxiao Wang; Jiongmin Yong
    Abstract: We investigate a linear quadratic stochastic zero-sum game where two players lobby a political representative to invest in a wind turbine farm. Players are time-inconsistent because they discount performance with a non-constant rate. Our objective is to identify a consistent planning equilibrium in which the players are aware of their inconsistency and cannot commit to a lobbying policy. We analyze the equilibrium behavior in both single-player and two-player cases and compare the behavior of the game under constant and non-constant discount rates. The equilibrium behavior is provided in closed-loop form, either analytically or via numerical approximation. Our numerical analysis of the equilibrium reveals that strategic behavior leads to more intense lobbying without resulting in overshooting.
    Date: 2023–04
  5. By: Maximilian Andres
    Abstract: So far, the theory of equilibrium selection in the infinitely repeated prisoner's dilemma is insensitive to communication possibilities. To address this issue, we incorporate the assumption that communication reduces -- but does not entirely eliminate -- an agent's uncertainty that the other agent follows a cooperative strategy into the theory. Because of this, agents still worry about the payoff from cooperating when the other one defects, i.e. the sucker's payoff S, and, games with communication are more conducive to cooperation than games without communication. This theory is supported by data from laboratory experiments, and by machine learning based evaluation of the communication content.
    Date: 2023–04
  6. By: NAKAMURA, Kensei
    Date: 2023–04–22
  7. By: Ngoc Thao NOET (GRANEM - Groupe de Recherche Angevin en Economie et Management - UA - Université d'Angers - Institut Agro Rennes Angers - Institut Agro - Institut national d'enseignement supérieur pour l'agriculture, l'alimentation et l'environnement); Serge Blondel (LIRAES (URP_ 4470) - Laboratoire Interdisciplinaire de Recherche Appliquée en Economie de la Santé - UPCité - Université Paris Cité, GRANEM - Groupe de Recherche Angevin en Economie et Management - UA - Université d'Angers - Institut Agro Rennes Angers - Institut Agro - Institut national d'enseignement supérieur pour l'agriculture, l'alimentation et l'environnement)
    Abstract: Using a contingent valuation approach over 114 subjects, we assess the degree of cooperation and explain the factors underlying ethical choices. Implementing the prisoners' dilemma and public good games reveals a correlation between the amount of the ethical premium and the degree of cooperation. We identify factors that increase this cooperation, such as the frequency of interactions with individuals. The more cooperative individuals are, the higher the ethical premium. In addition, individuals naturally seek to cooperate. The more the game is repeated, the higher the degree of cooperation. According to the items, the degree of contribution is lower when dilution of responsibility occurs.
    Keywords: cooperation, ethical values, public good game, prisoners' dilemma
    Date: 2023–01–01
  8. By: Jian Yang
    Abstract: We are concerned with the stability of a coalitional game, i.e., a transferable-utility (TU) cooperative game. First, the concept of core can be weakened so that the blocking of changes is limited to only those with multilateral backings. This principle of consensual blocking, as well as the traditional core-defining principle of unilateral blocking and one straddling in between, can all be applied to partition-allocation pairs. Each such pair is made up of a partition of the grand coalition and a corresponding allocation vector whose components are individually rational and efficient for the various constituent coalitions of the given partition. For the resulting strong, medium, and weak stability concepts, the first is core-compatible in that the traditional core exactly contains those allocations that are associated through this strong stability concept with the all-consolidated partition consisting of only the grand coalition. Probably more importantly, the latter medium and weak stability concepts are universal. By this, we mean that any game, no matter how ``poor'' it is, has its fair share of stable solutions. There is also a steepest ascent method to guide the convergence process to a mediumly stable partition-allocation pair from any starting partition.
    Date: 2023–04
  9. By: Ostrovsky, Michael (Stanford U); Skrzypacz, Andy (Stanford U)
    Abstract: We revisit the classic result on the (non-)existence of pure-strategy Nash equilibria in the Generalized First-Price Auction for sponsored search advertising and show that the conclusion may be reversed when ads are ranked based on the product of stochastic quality scores and bid amounts, rather than solely on the latter. Moreover, the expected revenue in the pure strategy equilibrium of the Generalized First-Price Auction may substantially exceed that of the Generalized Second-Price Auction.
    Date: 2022–10
  10. By: Jian Yang
    Abstract: We deal with coalitional games possessing strictly positive values. Individually rational allocations of such a game has clear fractional interpretations. Many concepts, including the long-existing core and other stability notions more recently proposed by Yang \cite{Y22}, can all be re-cast in this fractional mode. The latter allows a certain ranking between games, which we deem as in the sense of ``centripetality'', to imply a clearly describable shift in the games' stable solutions. %These trends would be preserved after the imposition of the restriction that fractions be positive as well. When coalitions' values are built on both random outcomes and a common positively homogeneous reward function characterizing players' enjoyments from their shares, the above link could help explain why aversion to risk often promotes cooperation.
    Date: 2023–04
  11. By: Matteo Escud\'e
    Abstract: I study a model of information acquisition and transmission in which the sender's ability to misreport her findings is limited. In equilibrium, the sender only influences the receiver by choosing to remain selectively ignorant, rather than by deceiving her about the discoveries. Although deception does not occur, I highlight how deception possibilities determine what information the sender chooses to acquire and transmit. I then turn to comparative statics, characterizing in which sense the sender benefits from her claims being more verifiable, showing this is akin to increasing her commitment power. Finally, I characterize sender- and receiver-optimal falsification environments.
    Date: 2023–04
  12. By: Noblit, Graham Alexander; Henrich, Joseph
    Abstract: Understanding how humans successfully stabilize public good contributions is a major ongoing question in the social and behavioral sciences. The use of targeted sanctions against defecting strategies is an important solution to this problem. However, ethnographic and behavioral evidence suggest that punishment is sometimes not used against defectors to stabilize cooperation. Sanctions instead are either light and insufficient to coerce cooperation or take the form of verbal repudiations, urging defectors to reform their behavior. Should defectors not reform, they are then ostracized from groups. We construct a cultural evolutionary game-theoretic model to study the evolution of ostracizing strategies in public goods games. We demonstrate that simple ostracizing strategies are unlikely to be evolutionarily viable and can neither encourage the evolution of contrite-defectors, who respond to punishment with cooperation, nor can invade recalcitrant-defecting populations, which ignore punishment. Motivated by the ethnographic literature, we then consider a hybrid sanctioning-ostracizing strategy that lightly-sanctions defectors before ostracizing repeat defectors. Such a strategy demonstrates clear advantages over simple sanctioning strategies. It can afford to impose light-sanctions when common because these sanctions are irrelevant when coercing future cooperation from defectors. More so, when recalcitrant defecting strategies have some possibility of arising in a population, sanctioning-ostracizing strategies dominate pure sanctioning ones, stabilizing cooperation with greater efficiency. Finally, our model makes psychological predictions concerning the reasoning processes that defectors will go through when defectors are coerced to cooperate by the threat of ostracism as opposed to sanctioning.
    Date: 2023–04–15
  13. By: Miguel Risco
    Abstract: In today’s world, social networks have a significant impact on information processes, shaping individuals’ beliefs and influencing their decisions. This paper proposes a model to understand how boundedly rational (DeGroot) individuals behave when seeking information to make decisions in situations where both social communication and private learning take place. The model assumes that information is a local public good, and individuals must decide how much effort to invest in costly information sources to improve their knowledge of the state of the world. Depending on the network structure and agents’ positions, some individuals will invest in private learning, while others will free-ride on the social supply of information. The model shows that multiple equilibria can arise, and uniqueness is controlled by the lowest eigenvalue of a matrix determined by the network. The lowest eigenvalue roughly captures how two-sided a network is. Two-sided networks feature multiple equilibria. Under a utilitarian perspective, agents would be more informed than they are in equilibrium. Social welfare would be improved if influential agents increased their information acquisition levels.
    Keywords: Information Acquisition, Learning, Public Goods, Network Effects, Information Diffusion, Bounded Rationality
    JEL: C72 D61 D83 D85 H41
    Date: 2023–04
  14. By: Noblit, Graham Alexander; Hadfield, Gillian
    Abstract: Human life is riddled with norms, many though not all of which are costly for individuals to adopt. Similarly, human ecological adaptation relies on costly-behaviors that often generate non-rivalrous and non-exclusionary benefits for group-members. Yet, in a dynamic world, innovations, environmental change, and information-revelation mean that what norms are beneficial for a group to adopt will inevitably change over time. However, multiple game-theoretic models studying the various mechanisms stabilizing normative behaviors have demonstrated that the stability of a norm does not depend on the benefits it confers. In turn, explanations of normative change have either relied on group-selective mechanisms to explain the presence of adaptive norms or have failed to identify conditions under which normative change occurs. We study normative change by means of costly-punishment and conflict resolution. We identify social differentiation in goals and punishment capacity as a key condition permitting normative change. While normative change that results from such social differentiation need not be group beneficial it will be beneficial to some subset of agents in the population. We additionally discuss how the intra-societal forces of normative conflict that we study might interact with group-selective forces and in turn determine the dynamics and outcomes of group-selection.
    Date: 2023–04–20
  15. By: Bhowmik, Anuj; Saha, Sandipan
    Abstract: The paper tries to answer one of the more nascent questions in the literature on general equilibrium theory by investigating the equivalence between the set of club equilibrium states and the bargaining set for a club economy. Clubs in this framework are treated in a parallel fashion to private goods as articles of choice. Each club membership is composed of three components: (i) the individual's characteristics; (ii) the profile of the club. and (iii) the club project. Thus clubs are identified through their profile and the particular project they undertake. We introduce the bargaining set for such an economy in lieu of Mas-Colell \cite{Mas : 89} and define a two-step veto mechanism. In this paper we establish that non-equilibrium states are those against which there exist a set of agents who agree upon a mutually beneficial trade agreement amongst themselves or in other words there exists a Walrasian objection to such states. In what follows from the literature is that Walrasian objections are justified as well which thereby helps us establish our equivalence.
    Keywords: Club goods, Bargaining set, Walrasian objection, Justified objection, Bargaining-Equilibrium equivalence.
    JEL: D5 D6 D62 H4
    Date: 2023–04–29
  16. By: Awad, Emiel; Minaudier, Clement
    Abstract: Interest groups are often highly selective regarding which policymakers to meet and when to meet them. How valuable are private meetings with policymakers as a function of their preferences and bargaining power, and when do interest group prefer access early or late in the legislative process? To answer these questions, we study a model of informational lobbying with a collective decision-making body and endogenous reforms. We show that the value of gaining private access to legislators depends not only on their ideological alignment with the interest group, but also on their ideological alignment with the median of the legislature and with the agenda setter. Moreover, the value of access to a particular legislator depends on the ideological alignment between the median and the agenda setter, even when that legislator is neither of them. Finally, we show that the agenda setter herself may not be a particularly valuable target and that she can be influenced by a simple cheap talk recommendation even though the interest group has transparent motives.
    Date: 2023–04–07
  17. By: Cordoba, Juan Carlos; Liu, Xiying
    Abstract: We develop a tractable general equilibrium model of oligopolistic competition that allows for endogenous product differentiation and exhibits various forms of competition, ranging from perfect to monopolistic competition, simultaneously. Our unified framework provides a novel way to integrate industrial organization with other fields, such as macroeconomics and trade. Our key contribution is the introduction of ex-ante heterogeneity, in contrast to the ex-post heterogeneity typically assumed in the literature (Metlitz, 2003). As a result, most firms in our model prefer to engage in face-to-face competition rather than creating their own variety, in contrast to monopolistic models. We characterize the free entry Cournot equilibrium, as well as the efficient and constrained efficient allocations. Our unified approach enables us to generalize existing results, challenge others, andshed new light on several long-standing economic issues, such as the Kaldor-Chamberlin controversy, the competitive effects of trade, and the strengths and weaknesses of monopolistically competitive models.
    Date: 2023–03–23
  18. By: Sarah Auster; Nicola Pavoni
    Abstract: We study the delegation problem between a principal and an agent, who not only has better information about the performance of the available actions but also superior awareness of the set of actions that are actually feasible. We provide conditions under which the agent finds it optimal to leave the principal unaware of relevant options. By doing so, the agent increases the principal’s cost of distorting the agent’s choices and increases the principal’s willingness to grant him higher information rents. We further show that the principal may use the option of renegotiation as a tool to implement actions that are not describable to her at the contracting stage. If the agent renegotiates, his proposal signals information about the payoff state. Due to her limited awareness, the principal makes a coarse inference from the agent’s recommendations and, as a result, accepts a large number of the agent’s proposals, which ultimately benefits both.
    Keywords: Unawareness, optimal delegation, strategic disclosure
    JEL: D82 D83 D86
    Date: 2023–04
  19. By: Elliott Hughes; Richard Watt (University of Canterbury)
    Abstract: In the USA, the remuneration for songwriters whose copyrighted material is broadcast using online interactive music services is subject to a compulsory license with a rate that is regulated by the Copyright Royalty Board (CRB). On the other hand, an essentially equally necessary input to the interactive music services, namely the sound recording copyright, is fully and freely negotiated between the parties. This situation sets up an interesting bargaining problem that should be of great interest to the CRB for their statutory mandate. The present paper sets out this problem formally, and resolves the equilibrium outcomes. The model is calibrated with the actual rates that have been set recently by the CRB.
    Keywords: Bargaining theory, regulation of copyright remuneration, Copyright Royalty Board USA
    JEL: D D04 D45
    Date: 2023–05–01
  20. By: Victor Augias (ECON - Département d'économie (Sciences Po) - Sciences Po - Sciences Po - CNRS - Centre National de la Recherche Scientifique); Daniel M A Barreto (Département d'économie - UPP - Université Pascal Paoli)
    Abstract: We analyze a model of persuasion in which Receiver forms wishful non-Bayesian beliefs. The effectiveness of persuasion depends on Receiver's material stakes: it is more effective when intended to encourage risky behavior that potentially lead to a high payoff and less effective when intended to encourage more cautious behavior. We illustrate this insight with applications showing why informational interventions are often ineffective in inducing greater investment in preventive health treatments, how financial advisors might take advantage of their clients overoptimistic beliefs and why strategic information disclosure to voters with different partisan preferences can lead to belief polarization in an electorate.
    Keywords: Non-Bayesian persuasion, Motivated thinking, Overoptimism, Optimal beliefs
    Date: 2022–02–15
  21. By: Bimpikis, Kostas (Stanford U); Morgenstern, Ilan (Stanford U); Saban, Daniela (Stanford U)
    Abstract: We explore the welfare implications of data-tracking technologies that enable firms to collect consumer data and use it for price discrimination. The model we develop centers around two features: competition between firms and consumers' level of sophistication. Our baseline environment features a firm that can collect information about the consumers it transacts with in a duopoly market, which it can then use in a second, monopoly market. We characterize and compare the equilibrium outcomes in three settings: (i) an economy with myopic consumers, who, when making purchase decisions, do not internalize the fact that firms track their behavior and use this information in future transactions, (ii) an economy with forward-looking consumers, who take into account the implications of data tracking when determining their actions, and (iii) an economy where no data-tracking technologies are used due to technological or regulatory constraints. We find that the absence of data tracking may lead to a decrease in consumer surplus, even when consumers are myopic. Importantly, this result relies critically on competition: consumer surplus may be higher when data-tracking technologies are used only when multiple firms offer substitutable products.
    Date: 2022–11

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