nep-gth New Economics Papers
on Game Theory
Issue of 2020‒11‒23
23 papers chosen by
Sylvain Béal
Université de Franche-Comté

  1. Asymmetric Guessing Games By AKIN, ZAFER
  2. On Convexity in Games with Externalities By José María Alsonso-Maijide; Mikel Álvarez-Mozos; María Gloria Fiestras-Janeiro; Andrés Jiménez-Losada
  3. The Frequency of Convergent Games under Best-Response Dynamics By Samuel C. Wiese; Torsten Heinrich
  4. Assortative multisided assignment games. The extreme core points By F.Javier Martínez de Albéniz; Carlos Rafels; Neus Ybern
  5. Naive Analytics Equilibrium By Berman, Ron; Heller, Yuval
  6. Trust and Reputation under Asymmetric Information By Janas, Moritz; Oljemark, Emilia
  7. Generosity during Covid-19 the effect of social distancing and framing on donations in dictator games By Lotti, Lorenzo
  8. Inequality in minimum-effort coordination By Feldhaus, Christoph; Rockenbach, Bettina; Zeppenfeld, Christopher
  9. Making the Most of Limited Government Capacity: Theory and Experiment By Sylvain Chassang; Lucia Del Carpio; Samuel Kapon
  10. Incomplete-Information Games in Large Populations with Anonymity By Martin F. Hellwig
  11. When "Better" is better than "Best" By Ben Amiet; Andrea Collevecchio; Kais Hamza
  12. Designing Contests Between Heterogeneous Contestants: An Experimental Studie of Tie-Breaks and Bid-Caps in All-Pay Auctions By Llorente-Saguer, Aniol; Sheremeta, Roman; Szech, Nora
  13. Second-Chance Offers and Buyer Reputation: Theory and Evidence on Auctions with Default By Engelmann, Dirk; Koch, Alexander K.; Frank, Jeff; Valente, Marieta
  14. Multiscale Control of Stackelberg Games By Michael Herty; Sonja Steffensen; Anna Th\"unen
  15. Dynamic Pricing of New Products in Competitive Markets: A Mean-Field Game Approach By Régis Chenavaz; Corina Paraschiv; Gabriel Turinici
  16. Coordinating to avoid the catastrophe By Bühl, Vitus; Schmidt, Robert C.
  17. Social preferences across different populations: Meta-analyses on the ultimatum game and dictator game By Francois Cochard; François Cochard; Julie Le Gallo; Nikolaos Georgantzis; Jean-Christian Tisserand
  18. Price of Anarchy of Simple Auctions with Interdependent Values By Alon Eden; Michal Feldman; Inbal Talgam-Cohen; Ori Zviran
  19. A general framework for studying contests By Bastani, Spencer; Giebe, Thomas; Gürtler, Oliver
  20. Fighting for Lemons: The Encouragement Effect in Dynamic Contests with Private Information By Juan Beccuti; Marc Möller
  21. Lying and Mistrust in the Continuous Deception Game By Beck, Tobias
  22. Coalition Formation with Border Carbon Adjustment By Schopf, Mark
  23. Competition in Fund Management and Forward Relative Performance Criteria By Michail Anthropelos; Tianran Geng; Thaleia Zariphopoulou

  1. By: AKIN, ZAFER
    Abstract: This paper theoretically and experimentally investigates the behavior of asymmetric players in guessing games. The asymmetry is created by introducing k>1 replicas of one of the players. Two-player and restricted N-player cases are examined in detail. Based on the model parameters, the equilibrium is either unique in which all players choose zero or mixed in which the weak player (k=1) imitates the strong player (k>1). A series of experiments involving two and three-player repeated guessing games with unique equilibrium is conducted. We find that equilibrium behavior is observed less frequently and overall choices are farther from the equilibrium in two-player asymmetric games in contrast to symmetric games, but this is not the case in three-player games. Convergence towards equilibrium exists in all cases but asymmetry slows down the speed of convergence to the equilibrium in two, but not in three-player games. Furthermore, the strong players have a slight earning advantage over the weak players, and asymmetry increases discrepancy in choices (defined as the squared distance of choices from the winning number) in both games.
    Keywords: Guessing game, asymmetry, convergence, game theory, experimental economics
    JEL: C72 C92
    Date: 2020–10–20
  2. By: José María Alsonso-Maijide (Universidade de Santiago de Compostela); Mikel Álvarez-Mozos (Universitat de Barcelona); María Gloria Fiestras-Janeiro (Universidade de Vigo); Andrés Jiménez-Losada (Universidad de Sevilla)
    Abstract: We introduce new notions of superadditivity and convexity for games with coalitional externalities. We show parallel results to the classic ones for transferable utility games without externalities. In superadditive games the grand coalition is the most efficient organization of agents. The convexity of a game is equivalent to having non decreasing contributions to larger embedded coalitions. We also see that convex games can only have negative externalities.
    Keywords: Externalities, Partition function, Lattice, Superadditivity, Convexity, Contribution.
    JEL: C71
    Date: 2019
  3. By: Samuel C. Wiese; Torsten Heinrich
    Abstract: Generating payoff matrices of normal-form games at random, we calculate the frequency of games with a unique pure strategy Nash equilibrium in the ensemble of $n$-player, $m$-strategy games. These are perfectly predictable as they must converge to the Nash equilibrium. We then consider a wider class of games that converge under a best-response dynamic, in which each player chooses their optimal pure strategy successively. We show that the frequency of convergent games goes to zero as the number of players or the number of strategies goes to infinity. In the $2$-player case, we show that for large games with at least $10$ strategies, convergent games with multiple pure strategy Nash equilibria are more likely than games with a unique Nash equilibrium. Our novel approach uses an $n$-partite graph to describe games.
    Date: 2020–11
  4. By: F.Javier Martínez de Albéniz (Universitat de Barcelona); Carlos Rafels (Universitat de Barcelona); Neus Ybern (Universitat Politècnica de Catalunya)
    Abstract: We analyze assortative multisided assignment games, following Sherstyuk (1999) and Martínez-de-Albéniz et al. (2019). In them players’ abilities are complementary across types (i.e. supermodular), and also the output of the essential coalitions is increasing depending on types. We study the extreme core points and show a simple mechanism to compute all of them. In this way we describe the whole core. This mechanism works from the original data array and the maximum number of extreme core points is obtained.
    Keywords: Assortative market, assignment game, multisided assignment game, core, extreme core allocations.
    JEL: C71
    Date: 2019
  5. By: Berman, Ron; Heller, Yuval
    Abstract: We study interactions with uncertainty about demand sensitivity. In our solution concept (1) firms choose seemingly-optimal strategies given the level of sophistication of their data analytics, and (2) the levels of sophistication form best responses to one another. Under the ensuing equilibrium firms underestimate price elasticities and overestimate advertising effectiveness, as observed empirically. The misestimates cause firms to set prices too high and to over-advertise. In games with strategic complements (substitutes), profits Pareto dominate (are dominated by) those of the Nash equilibrium. Applying the model to team production games explains the prevalence of overconfidence among entrepreneurs and salespeople.
    Keywords: Advertising, pricing, data analytics, strategic distortion, strategic complements, indirect evolutionary approach.
    JEL: C73 D43 M37
    Date: 2020–10–28
  6. By: Janas, Moritz; Oljemark, Emilia
    Abstract: We study the role of information about the multiplier in a finitely repeated investment game. A high multiplier increases the reputational incentives of a trustee, leading to more repayments. Our perfect Bayesian equilibrium analysis shows that if the trustee is privately informed about the multiplier, both the expected frequency of investments and repayments as well as the expected payoffs of both players are higher compared to a situation where the multiplier is public knowledge. We test this result in a laboratory experiment. The data cannot confirm the predicted welfare dominance of private information about the multiplier. We discuss potential reasons for the deviation between theory and experimental data.
    Keywords: reputation,trust,incomplete information,experiment
    JEL: C73 C92 D82 D83 M13
    Date: 2020
  7. By: Lotti, Lorenzo
    Abstract: This paper investigates the impact of prolonged social distancing on generosity by analyzing the responses of 1255 US citizens to dictator games spread out over eight weeks of the early stages of the COVID-19 pandemic. Despite the isolation and the negative effects on employment and household finances, individuals became more generous over this time period. There is significant heterogeneity in the effect of additional regressors,such as perceived contagion risk, on the likelihood and amount donated to strangers,family members, or the government. At the same time, significant effects of the position of games with respect to the others highlight the significant role of framing on generous behaviours.
    Keywords: Generosity, Dictator Game, Social Preferences, Framing, Altruism, Covid-19
    JEL: C71 D63 D64 D71 D91 I14
    Date: 2020–10–28
  8. By: Feldhaus, Christoph; Rockenbach, Bettina; Zeppenfeld, Christopher
    Abstract: Successful coordination is key for economic and societal wealth. The rich literature on the minimum-effort game (MEG) has provided valuable insights into coordination, both theoretically and empirically. Yet, although real-world scenarios often involve asymmetric benefits and/or costs from coordination, most previous studies rely on symmetric MEGs. We investigate the effect of unequal equilibrium pay-offs in the MEG. In two experiments, we observe that players are better able to coordinate on an equal rather than an unequal Pareto-dominant equilibrium. We find that the ability to coordinate on the unequal Pareto-dominant equilibrium critically hinges on the costs of miscoordination for the player who benefits most from successful coordination: when her costs are low, she seems able to stabilize the Pareto-dominant equilibrium even if payoffs are highly unequal, whereas coordination success worsens substantially when her costs are high.
    Keywords: minimum effort game,coordination,social comparison,potential games,lab experiment
    JEL: C72 C92
    Date: 2020
  9. By: Sylvain Chassang; Lucia Del Carpio; Samuel Kapon
    Abstract: Limits on a government’s capacity to enforce laws can result in multiple equilibria. If most agents comply, limited enforcement is sufficient to dissuade isolated agents from misbehaving. If most agents do not comply, overstretched enforcement capacity has a minimal impact on behavior. We study the extent to which divide-and-conquer enforcement strategies can help select a high compliance equilibrium in the presence of realistic compliance frictions. We study the role of information about the compliance of others both in theory and in lab experiments. As the number of agents gets large, theory indicates that providing information or not is irrelevant in equilibrium. In contrast, providing individualized information has a first order impact in experimental play by increasing convergence to equilibrium. This illustrates the value of out-of-equilibrium information design.
    JEL: C72 C73 C92 D73 D82 D86 H26
    Date: 2020–10
  10. By: Martin F. Hellwig (Max Planck Institute for Research on Collective Goods, Bonn)
    Abstract: The paper provides theoretical foundations for models of strategic interdependence under uncertainty that have a continuum of agents and a decomposition of uncertainty into a macro component and an agent-specific micro component, with a law of large numbers for the latter. The decomposition of uncertainty is implied by a condition of exchangeability of agents' types, which is imposed equivalently imposed at the level of the prior or at the level of beliefs, i.e., posteriors. Under an additional condition of anonymity in payoffs, agents' behaviors are fully determined by their macro beliefs about the cross-section distribution of types and by the cross-section distribution of other agents' strategies. Any probability distribution over cross-section distributions of types is admissible, but not every macro belief function is compatible with a common prior.
    Keywords: Incomplete-information games, large populations, belief functions, common priors, exchangeability, conditional independence, conditional exact law of large numbers
    JEL: C70 D82 D83
    Date: 2020–08
  11. By: Ben Amiet; Andrea Collevecchio; Kais Hamza
    Abstract: We consider two-player normal form games where each player has the same finite strategy set. The payoffs of each player are assumed to be i.i.d. random variables with a continuous distribution. We show that, with high probability, the better-response dynamics converge to pure Nash equilibrium whenever there is one, whereas best-response dynamics fails to converge, as it is trapped.
    Date: 2020–10
  12. By: Llorente-Saguer, Aniol; Sheremeta, Roman; Szech, Nora
    Abstract: Contests are well-established mechanisms for political lobbying, innovation, rentseeking, incentivizing workers, and advancing R&D. A well-known theoretical result in the contest literature is that greater heterogeneity decreases investments of contestants because of the "discouragement effect." Leveling the playing field by favoring weaker contestants through strict bid-caps and favorable tie-breaking rules can reduce discouragement and increase the designer's revenue. We test these predictions in a laboratory experiment. Our data confirm that placing bid-caps and using favorable tie-breaking rules significantly diminishes discouragement in weaker contestants. The impact on revenue is more intricate. In contrast to theory, a strict bid-cap does not increase revenue, but a mild bid-cap can increase revenue even when not predicted by theory. Our data also show that tie-breaking rules seem to have little impact on the designer's revenue: the encouragement of weaker contestants is offset by stronger contestants competing less aggressively. We discuss deviations from the Nash predictions in light of different behavioral approaches.
    Keywords: all-pay auction,rent-seeking,lobbying,bid-caps,tie-breaks,contest design
    JEL: C72 C91 D72
    Date: 2020
  13. By: Engelmann, Dirk; Koch, Alexander K.; Frank, Jeff; Valente, Marieta
    Abstract: Winning bidders in online auctions frequently fail to complete the transaction. Because enforcing bids usually is too costly, auction platforms often allow sellers to make a "secondchance" offer to the second highest bidder, to buy at the bid price of this bidder, and let sellers leave negative feedback on buyers who fail to pay. We show theoretically that, all else equal, the availability of second-chance offers reduces amounts bid in auctions where there is a probability that a bidder defaults. Nevertheless, we show that it is not optimal for a seller to exclude a buyer who is likely to default. In addition, buyer reputation systems create a strategic effect that rewards bidders who have a reputation for defaulting, counter to the idea of creating a deterrent against such behavior. Actual bidding in experimental auctions support these predictions and provide insights on their practical relevance.
    Keywords: Auctions,Default,Reputation,Second-Chance Offers
    JEL: D44
    Date: 2020
  14. By: Michael Herty; Sonja Steffensen; Anna Th\"unen
    Abstract: We present a linear--quadratic Stackelberg game with a large number of followers and we also derive the mean field limit of infinitely many followers. The relation between optimization and mean-field limit is studied and conditions for consistency are established. Finally, we propose a numerical method based on the derived models and present numerical results.
    Date: 2020–11
  15. By: Régis Chenavaz (LTCI - Laboratoire Traitement et Communication de l'Information - Télécom ParisTech - IMT - Institut Mines-Télécom [Paris] - CNRS - Centre National de la Recherche Scientifique); Corina Paraschiv (GREGH - Groupement de Recherche et d'Etudes en Gestion à HEC - HEC Paris - Ecole des Hautes Etudes Commerciales - CNRS - Centre National de la Recherche Scientifique, IUF - Institut Universitaire de France - M.E.N.E.S.R. - Ministère de l'Education nationale, de l’Enseignement supérieur et de la Recherche); Gabriel Turinici (CEREMADE - CEntre de REcherches en MAthématiques de la DEcision - Université Paris Dauphine-PSL - PSL - Université Paris sciences et lettres - CNRS - Centre National de la Recherche Scientifique, IUF - Institut Universitaire de France - M.E.N.E.S.R. - Ministère de l'Education nationale, de l’Enseignement supérieur et de la Recherche)
    Abstract: Dynamic pricing of new products has been extensively studied in monopolistic and oligopolistic markets. But, the optimal control and differential game tools used to investigate the pricing behavior on markets with a finite number of firms are not well-suited to model competitive markets with an infinity of firms. Using a mean-field games approach, this paper examines dynamic pricing policies in competitive markets, where no firm exerts market power. The theoretical setting is based on a diffusion modeì a la Bass. We prove both the existence and the uniqueness of a mean-field game equilibrium, and we investigate mean tendencies and firms dispersion in the market. Numerical simulations show that the competitive market splits into two separate groups of firms depending on their production experience. The two groups differ in price and profit. Thus, high prices and profits do not have to signal anticompetitive practices, stimulating the debate on market regulation.
    Keywords: competitive markets,mean-field games,Dynamic pricing,new products diffusion
    Date: 2020–11–01
  16. By: Bühl, Vitus; Schmidt, Robert C.
    Abstract: In the presence of a tipping point for dangerous climate damages, the cooperation problem of climate protection can be transformed into a coordination problem that is much easier to deal with (Barrett, 2013). This holds in particular if the amount of greenhouse gas emissions that triggers the catastrophe is precisely known, while the well-known free-rider problem re-appears if the location of the threshold is sufficiently uncertain. In this paper, we focus on the question how the non-signatories (outsiders of a climate agreement) coordinate to avoid the catastrophe, if the tipping point is known. In particular, in light of a multiplicity of equilibria in this coordination problem, the assumption that outsiders will always successfully coordinate to avoid the threshold, even if this is in their collective interest, seems overly optimistic. We analyze how the probability that the outsiders coordinate on an equilibrium in which the threshold is avoided, affects the incentives of countries to join the climate coalition. In some cases, there are multiple equilibria at the participation stage: an equilibrium with full participation, and an equilibrium in which a much smaller coalition forms - just large enough to achieve an outcome in which the catastrophe is avoided with positive probability.
    Keywords: tipping point,climate catastrophe,coordination game,international environmental agreement,climate cooperation
    JEL: D62 F53 Q54
    Date: 2020
  17. By: Francois Cochard (CRESE - Centre de REcherches sur les Stratégies Economiques (EA 3190) - UFC - Université de Franche-Comté - UBFC - Université Bourgogne Franche-Comté [COMUE]); François Cochard; Julie Le Gallo (CESAER - Centre d'Economie et de Sociologie Rurales Appliquées à l'Agriculture et aux Espaces Ruraux - AgroSup Dijon - Institut National Supérieur des Sciences Agronomiques, de l'Alimentation et de l'Environnement - INRAE - Institut National de Recherche pour l’Agriculture, l’Alimentation et l’Environnement); Nikolaos Georgantzis (CEREN - Centre de Recherche sur l'ENtreprise [Dijon] - BSB - Burgundy School of Business (BSB) - Ecole Supérieure de Commerce de Dijon Bourgogne (ESC)); Jean-Christian Tisserand (CEREN - Centre de Recherche sur l'ENtreprise [Dijon] - BSB - Burgundy School of Business (BSB) - Ecole Supérieure de Commerce de Dijon Bourgogne (ESC))
    Abstract: We perform meta-regressions on a single database containing 96 observations of simple ultimatum games and 144 observations of simple dictator games to disentangle the fairness hypothesis based on the degree of economic development of a country. According to the fairness hypothesis, o ers in the two games should not di er if they were motivated by a subject's fairness concerns. Using the di erence across countries between o ers in ultimatum and dictator games, we address the e ect of being exposed to the market mechanism on pure fairness concerns and other-regarding, expectations-driven fairness. Our results show in particular that the lower the level of economic development in a country, the less likely the rejection of the fairness hypothesis.
    Keywords: ultimatum game,dictator game,meta-analysis,social preferences,social preferences JEL Classification: C13,C78,D03,D64
    Date: 2021–02
  18. By: Alon Eden; Michal Feldman; Inbal Talgam-Cohen; Ori Zviran
    Abstract: We expand the literature on the price of anarchy (PoA) of simultaneous item auctions by considering settings with correlated values; we do this via the fundamental economic model of interdependent values (IDV). It is well-known that in multi-item settings with private values, correlated values can lead to bad PoA, which can be polynomially large in the number of agents $n$. In the more general model of IDV, we show that the PoA can be polynomially large even in single-item settings. On the positive side, we identify a natural condition on information dispersion in the market, termed $\gamma$-heterogeneity, which enables good PoA guarantees. Under this condition, we show that for single-item settings, the PoA of standard mechanisms degrades gracefully with $\gamma$. For settings with $m>1$ items we show a separation between two domains: If $n \geq m$, we devise a new simultaneous item auction with good PoA (with respect to $\gamma$), under limited information asymmetry. To the best of our knowledge, this is the first positive PoA result for correlated values in multi-item settings. The main technical difficulty in establishing this result is that the standard tool for establishing PoA results -- the smoothness framework -- is unsuitable for IDV settings, and so we must introduce new techniques to address the unique challenges imposed by such settings. In the domain of $n \ll m$, we establish impossibility results even for surprisingly simple scenarios.
    Date: 2020–11
  19. By: Bastani, Spencer; Giebe, Thomas; Gürtler, Oliver
    Abstract: We develop a general framework to study contests, containing the well-known models of Tullock (1980) and Lazear & Rosen (1981) as special cases. The contest outcome depends on players' effort and skill, the latter being subject to symmetric uncertainty. The model is tractable, because a symmetric equilibrium exists under general assumptions regarding production technologies and skill distributions. We construct a link between our contest model and expected utility theory and exploit this link to revisit important comparative statics results of contest theory and show how these can be overturned. Finally, we apply our results to study optimal workforce composition.
    Keywords: contest theory,symmetric equilibrium,heterogeneity,risk,decision theory
    JEL: C72 D74 D81 J23 M51
    Date: 2020
  20. By: Juan Beccuti; Marc Möller
    Abstract: This paper proposes a tractable model of a dynamic contest where players have private information about the contest’s prize. We show that private information helps to encourage players who have fallen behind, leading to an increase in aggre- gate incentives. We derive the optimal information design for a designer interested in the maximization of aggregate effort. Optimal signals turn out to be private and imperfectly informative and aim to level the playing field at any stage of the dynamic interaction.
    Keywords: Dynamic contests, discouragement effect, information design
    JEL: C72 D72 D82
    Date: 2020–11
  21. By: Beck, Tobias
    Abstract: I present a novel experimental design to measure lying and mistrust as continuous variables on an individual level. My experiment is a sender-receiver game framed as an investment game. It features two players: firstly, an advisor with complete information (i.e., the sender) who is incentivized to lie about the true value of an optimal investment and, secondly, an investor with incomplete information (i.e., the receiver) who is incentivized to invest optimally and therefore must rely on the alleged optimum reported by the advisor. Due to its continuous message space, this experiment allows observing more differentiated behavior and therefore enables testing of more sophisticated theoretical predictions. I find that the senders lie by overstating the true value of the optimum to an average extent of about 148%, while the receivers suspect them to do so by only 56%. Moreover, my results indicate that the senders make strategic considerations about their potential to manipulate others when deciding about the sizes of their lies. However, I find that the size of the lie and the size of mistrust do not only matter from a strategic perspective but also have an impact on how people perceive their own behavior. Consistent with previous studies, my findings support the conjecture that lying costs increase with the size of the lie. Beyond that, I provide evidence for some endogenous preference for trust. Both players’ behaviors and beliefs are consistent over time. In addition, my classification of both players’ strategies is consistent with their self-assessment of their behavior within the experiment.
    Keywords: Size of the lie,Size of mistrust,Honesty,Deception Game,Investments,Asymmetric information,Experimental design
    JEL: C91 D01 D82
    Date: 2020
  22. By: Schopf, Mark
    Abstract: The present paper analyzes the impact of a climate coalition's border carbon adjustment on emissions from commodity production, welfare and the coalition size. The coalition implements border carbon adjustment to reduce carbon leakage and to improve its terms of trade, while the fringe abstains from any trade policy. With symmetric countries, the optimal import tax or export subsidy is positive but smaller than the coalition's implicit emission price. With a linear-quadratic specification, the coalition exports the commodity. Total emissions decrease with the coalition size, and total welfare increases [decreases] with the coalition size if the coalition is large [small]. Then, the reduced climate costs outweigh [are outweighed by] the increased trade distortions. The unique stable coalition consists of three or more countries, including the grand coalition, and raises the welfare of each country compared to the business-as-usual equilibrium. If no [each] country implements a trade policy, the stable coalition consists of two [three] or less countries. Compared to the case in which only the coalition implements border carbon adjustment, the welfare of each country is reduced [if the stable coalition then consists of four or more countries]. All results are derived analytically.
    Keywords: Carbon Leakage,Climate Change,Environmental Policy,Nash Equilibrium,Terms of Trade
    JEL: F13 F18 H23 Q54 Q56 Q58
    Date: 2020
  23. By: Michail Anthropelos; Tianran Geng; Thaleia Zariphopoulou
    Abstract: In an Ito-diffusion market, two fund managers trade under relative performance concerns. For both the asset specialization and diversification settings, we analyze the passive and competitive cases. We measure the performance of the managers' strategies via forward relative performance criteria, leading to the respective notions of forward best-response criterion and forward Nash equilibrium. The motivation to develop such criteria comes from the need to relax various crucial, but quite stringent, existing assumptions -- such as, the a priori choices of both the market model and the investment horizon, the commonality of the latter for both managers as well as the full a priori knowledge of the competitor's policies for the best-response case. We focus on locally riskless criteria and deduce the random forward equations. We solve the CRRA cases, thus also extending the related results in the classical setting. An important by-product of the work herein is the development of forward performance criteria for investment problems in Ito-diffusion markets under the presence of correlated random endowment process for both the perfectly and the incomplete market cases.
    Date: 2020–11

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