nep-gth New Economics Papers
on Game Theory
Issue of 2020‒04‒27
thirteen papers chosen by
Sylvain Béal
Université de Franche-Comté

  1. Instability of Defection in the Prisoner’s Dilemma: Best Experienced Payoff Dynamics Analysis By Arigapudi, Srinivas; Heller, Yuval; Milchtaich, Igal
  2. Axiomatizations of Dutta-Ray's egalitarian solution on the domain of convex games By Calleja, Pedro; Llerena, Francesc; Sudhölter, Peter
  3. Self-Selection Into Strategic Environments By Guillaume HOLLARD; Fabien PEREZ
  4. Behavioral Equilibrium and Evolutionary Dynamics in Asset Markets By Igor V. Evstigneev; Thorsten Hens; Valeriya Potapova; Klaus Reiner Schenk-Hoppé
  5. Profit-enhancing entries in mixed oligopolies By Haraguchi, Junichi; Matsumura, Toshihiro
  6. A small volume reduction that melts down the market: Auctions with endogenous rationing By Ehrhart, Karl-Martin; Hanke, Ann-Katrin; Ott, Marion
  7. No-arbitrage commodity option pricing with market manipulation By Aïd, René; Callegaro, Giorgia; Campi, Luciano
  8. Adaptive Rationality in Strategic Interaction: Do Emotions Regulate Thinking about Others? By Timo Ehrig; Monica Jaison Manjaly; Aditya Singh; Shyam Sunder
  9. The ratchet effect in social dilemmas By Gallier, Carlo; Sturm, Bodo
  10. Commuting and internet traffic congestion By Berliant, Marcus
  11. Two-sided Strategic Information Transmission By Saori Chiba; Kazumi Hori
  12. Market for Information and Selling Mechanisms By David Bounies; Antoine Dubus; Patrick Waelbroeck
  13. A strictly economic explanation of gender norms: The lasting legacy of the plough By Alessandro Cigno

  1. By: Arigapudi, Srinivas; Heller, Yuval; Milchtaich, Igal
    Abstract: We study population dynamics under which each revising agent tests each strategy k times, with each trial being against a newly drawn opponent, and chooses the strategy whose mean payoff was highest. When k = 1, defection is globally stable in the prisoner’s dilemma. By contrast, when k > 1 we show that there exists a globally stable state in which agents cooperate with probability between 28% and 50%. Next, we characterize stability of strict equilibria in general games. Our results demonstrate that the empirically-plausible case of k > 1 can yield qualitatively different predictions than the case of k = 1 that is commonly studied in the literature.
    Keywords: learning, cooperation, best experienced payoff dynamics, sampling equilibrium, evolutionary stability
    JEL: C72 C73
    Date: 2020–04–11
  2. By: Calleja, Pedro (Departament de Matemàtica Econòmica, Financera i Actuarial); Llerena, Francesc (Departament de Gestió d'Empreses); Sudhölter, Peter (Department of Business and Economics)
    Abstract: We show that on the domain of convex games, Dutta-Ray's egalitarian solution is characterized by core selection, aggregate monotonicity, and bounded richness, a new property requiring that the poorest players cannot be made richer within the core. Replacing "poorest" by "poorer" allows to eliminate aggregate monotonicity. Moreover, strengthening core selection into bilateral consistency à la Davis and Maschler, and Pareto optimality into individual rationality and bilateral consistency à la Hart and Mas-Colell, we obtain alternative and stylized axiomatic approaches.
    Keywords: Dutta-Rays egalitarian solution; axiomatizations; convex TU game
    JEL: C71
    Date: 2020–04–16
  3. By: Guillaume HOLLARD (CREST Ecole polytechnique CNRS); Fabien PEREZ (CREST, INSEE)
    Abstract: Self-selection is common in naturally-occurring situations, including those where players can choose to engage in strategic interactions, but is absent from most lab experiments. A better understanding of the effect of self-selection will therefore enhance the external validity of behavioral game theory. We here gauge the impact of self-selection on strategic interactions in one-shot games by adding an explicit self-selection stage to a lab experiment so as to address our two main questions: (1) What are the determinants of self-selection? and (2) What are the consequences of self-selection on the composition of the pool of subjects and, in turn, on the strategies played? We consider three potential drivers of self-selection: risk aversion, past strategies and a new (in this context) measure of confidence. One side-product of the present study is thus the first assessment of the relevance of confidence judgments in experimental games. We find that risk-aversion and confidence explain a large part of the individual heterogeneity in self-selection. We also find a substantial change in the strategies used under self-selection (as compared to no self-selection), with the main effect coming from the filtering out of ”poor” strategies (i.e. dominated strategies or strategies leading to low payoffs). As a result, we can predict that self-selected subjects in the field act morein accordance with Nash-equilibrium predictions, although there are still large deviations from equilibrium.
    Keywords: Experiments; Self-selection; non-cooperative games; External Validity.
    JEL: C72 C9
    Date: 2020–04–11
  4. By: Igor V. Evstigneev (University of Manchester - Economics, School of Social Sciences); Thorsten Hens (University of Zurich - Department of Banking and Finance; Norwegian School of Economics and Business Administration (NHH); Swiss Finance Institute); Valeriya Potapova (University of Manchester - Economics, School of Social Sciences); Klaus Reiner Schenk-Hoppé (University of Manchester - Department of Economics; Norwegian School of Economics (NHH) - Department of Finance)
    Abstract: This paper analyzes a dynamic stochastic equilibrium model of an asset market based on behavioral and evolutionary principles. The core of the model is a non-traditional game-theoretic framework combining elements of stochastic dynamic games and evolutionary game theory. Its key characteristic feature is that it relies only on objectively observable market data and does not use hidden individual agents' characteristics (such as their utilities and beliefs). A central goal of the study is to identify an investment strategy that allows an investor to survive in the market selection process, i.e., to keep with probability one a strictly positive, bounded away from zero share of market wealth over an infinite time horizon, irrespective of the strategies used by the other players. The main results show that under very general assumptions, such a strategy exists, is asymptotically unique and easily computable.
    Keywords: Evolutionary finance, Behavioral finance, Stochastic dynamic games, DSGE, survival portfolio rules.
    JEL: C73 D53 D58 G11 G02
    Date: 2020–04
  5. By: Haraguchi, Junichi; Matsumura, Toshihiro
    Abstract: Mixed oligopolies are characterized by private and public enterprises. Entry into these markets was restrictive, but has now been relaxed by deregulations; as a result, private firms have entered mixed oligopolies. An increase in the number of private firms increases competition among private firms and reduces the profit of incumbent private firms, given the privatization policy remains unchanged. However, an increase in the number of private firms may in turn affect privatization policy, and thus, indirectly affect private firms' profits. Therefore, the overall effect on private firms' profit is ambiguous. In this study, we thus investigate how the number of private firms affects the profit of each private firm in mixed oligopolies. For this end, we use a linear-quadratic production cost function, which covers two popular model formulations in the mixed oligopoly literature. We show that, if the degree of privatization is exogenous, the profit of each private firm is decreasing in the number of private firms. However, if the degree of privatization is endogenous, the relationship between the number of private firms and profit takes an inverted-U shape under a plausible range of cost parameters. Our results imply that there can exist multiple equilibria in free-entry markets with different degrees of privatization.
    Keywords: optimal degree of privatization, profit-enhancing entry, multiple long-run stable equilibria
    JEL: D43 H44 L33
    Date: 2020–04–17
  6. By: Ehrhart, Karl-Martin; Hanke, Ann-Katrin; Ott, Marion
    Abstract: Auctions with endogenous rationing have been introduced to stimulate competition. Such (procurement) auctions reduce the volume put out to tender when competition is low. This paper finds a strong negative effect of endogenous rationing on participation when bid-preparation is costly, counteracting the aim to stimulate competition. For multiple auctioneer's objectives mentioned in directives, we derive optimal mechanisms, which differ due to different evaluation of the tradeoff between participation and bid-preparation costs. Thus, the auctioneer needs to decide on an objective. However, reducing bid-preparation costs improves the optimal values of multiple objective functions.
    Keywords: auction,participation,market design,optimal mechanism,renewable energy support
    JEL: D82 Q48 D47 D44
    Date: 2020
  7. By: Aïd, René; Callegaro, Giorgia; Campi, Luciano
    Abstract: We design three continuous-time models in finite horizon of a commodity price, whose dynamics can be affected by the actions of a representative risk-neutral producer and a representative risk-neutral trader. Depending on the model, the producer can control the drift and/or the volatility of the price whereas the trader can at most affect the volatility. The producer can affect the volatility in two ways: either by randomizing her production rate or, as the trader, using other means such as spreading false information. Moreover, the producer contracts at time zero a fixed position in a European convex derivative with the trader. The trader can be price-taker, as in the first two models, or she can also affect the volatility of the commodity price, as in the third model. We solve all three models semi-explicitly and give closed-form expressions of the derivative price over a small time horizon, preventing arbitrage opportunities to arise. We find that when the trader is price-taker, the producer can always compensate the loss in expected production profit generated by an increase of volatility by a gain in the derivative position by driving the price at maturity to a suitable level. Finally, in case the trader is active, the model takes the form of a nonzero-sum linear-quadratic stochastic differential game and we find that when the production rate is already at its optimal stationary level, there is an amount of derivative position that makes both players better off when entering the game.
    Keywords: price manipulation; fair game option pricing; martingale optimality principle; linear-quadratic stochastic differential games
    JEL: C73
    Date: 2020–04–02
  8. By: Timo Ehrig (Max Planck Institute for Mathematics in the Sciences, Leipzig); Monica Jaison Manjaly (Indian Institute of Technology, Gandhinagar); Aditya Singh (Indian Institute of Technology, Gandhinagar); Shyam Sunder (School of Management and Cowles Foundation, Yale University)
    Abstract: Forming beliefs or expectations about others’ behavior is fundamental to strategy, as it co-determines the outcomes of interactions in and across organizations. In the game theoretic conception of rationality, agents reason iteratively about each other to form expectations about behavior. According to prior scholarship, actual strategists fall short of this ideal, and attempts to understand the underlying cognitive processes of forming expectations about others are in their infancy. We propose that emotions help regulate iterative reasoning, that is, their tendency to not only reflect on what others think, but also on what others think about their thinking. Drawing on a controlled experiment, we ï¬ nd that a negative emotion (fear) deepens the tendency to engage in iterative reasoning, compared to a positive emotion (amusement). Moreover, neutral emotions yield even deeper levels of reasoning. We tentatively interpret these early ï¬ ndings and speculate about the broader link of emotions and expectations in the context of strategic management. Extending the view of emotional regulation as a capability, emotions may be building blocks of rational heuristics for strategic interaction and enable interactive decision-making when strategists have little experience with the environment.
    Date: 2020–04
  9. By: Gallier, Carlo; Sturm, Bodo
    Abstract: In this paper, we investigate whether dynamic incentive schemes lead to a ratchet effect in a social dilemma. We test whether subjects strategically restrict their contribution levels at the beginning of a cumulative public goods game in order to avoid high obligations in the future and how this affects efficiency. The incentive schemes prescribe that individual contributions have to be at least as high as, or strictly higher than, contributions in the previous period. We observe a substantial and statistically significant ratchet effect. Participants reduce their public good contribution levels at the beginning of the game, anticipating that higher contributions imply higher minimum contribution levels in the future, which increases the risk of being exploited by freeriders. While the dynamic incentive schemes lead to increasing contribution levels over the course of the game, this increase is not strong enough to compensate the efficiency losses at the beginning.
    Keywords: Public goods,dynamic incentives,minimum contribution rules,ratchet effect
    JEL: C72 C92 H41
    Date: 2020
  10. By: Berliant, Marcus
    Abstract: We examine the fine microstructure of commuting in a game-theoretic setting with a continuum of commuters. Commuters' home and work locations can be heterogeneous. A commuter transport network is exogenous. Traffic speed is determined by link capacity and by local congestion at a time and place along a link, where local congestion at a time and place is endogenous. The model can be reinterpreted to apply to congestion on the internet. We find sufficient conditions for existence of equilibrium, that multiple equilibria are ubiquitous, and that the welfare properties of morning and evening commute equilibria differ on a generalization of a directed tree.
    Keywords: Commuting; Internet traffic; Congestion externality; Efficient Nash equilibrium
    JEL: L86 R41
    Date: 2020–04–12
  11. By: Saori Chiba (Kyoto University, Graduate School of Economics); Kazumi Hori (Kyoto University, Graduate School of Economics)
    Abstract: We study a cheap talk model in which a decision maker and an expert are both privately informed. Both players observe independent signals that jointly determine ideal actions for the players. Furthermore, in our model, the decision maker can send a cheap talk message to the expert, which is followed by the expert’s cheap talk and then the decision maker’s decision making. We show that the informed decision maker can informatively reveal her private information to the expert but her talk does not affect the quality of the expert’s information transmission in models in which optimal actions are only additively or multiplicatively separable in the two players’ information, and their preferences are represented by quadratic loss functions. We also apply our finding to a decision maker’s information acquisition problem.
    Keywords: Cheap Talk, Two-Sided Asymmetric Information, Two-Way Communication
    JEL: D82 D83
    Date: 2020–04
  12. By: David Bounies; Antoine Dubus; Patrick Waelbroeck
    Abstract: We investigate the strategies of a data intermediary selling consumer information to firms for price discrimination purpose. We analyze how the mechanism through which the data intermediary sells information influences how much consumer information she will collect and sell to firms, and how it impacts consumer surplus. We consider three selling mechanisms tailored to sell consumer information: take it or leave it, sequential bargaining, and auctions. We show that the more information the intermediary collects, the lower consumer surplus. Consumer information collection is minimized, and consumer surplus maximized under the take it or leave it mechanism, which is the least profitable mechanism for the intermediary. We discuss two regulatory tools { a data minimization principle and a price cap { that can be used by data protection agencies and competition authorities to limit consumer information collection, increase consumer surplus, and ensure a fair access to information to firms.
    Date: 2020–04
  13. By: Alessandro Cigno
    Abstract: We show that the descendants of primeval plough users have an interest in maintaining the gender division of labour which was originally justi.ed on comparative-advantage grounds, even though in a modern economy individual productivity depends on education rather than physical characteristics. The result rests on the argument that the contract enforcement technology developed in response to the availability of the plough serves a purpose also in a modern economy because of a possible hold-up problem in the implementation of a Nash-bargaining equilibrium with domestic division of labour.
    Keywords: Plough, comparative advantage, matching, hold-up problem, migration.
    Date: 2020

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