nep-gth New Economics Papers
on Game Theory
Issue of 2020‒09‒07
eighteen papers chosen by
Sylvain Béal
Université de Franche-Comté

  1. A pure bargaining game of dynamic cake eating By Simon Hoof
  2. Spatial Iterated Prisoner's Dilemma as a Transformation Semigroup By Isaiah Farahbakhsh; Chrystopher L. Nehaniv
  6. Imposing Equilibrium Restrictions in the Estimation of Dynamic Discrete Games By Victor Aguirregabiria; Mathieu Marcoux
  8. Allocating Investments in Conglomerate Mergers: A Game Theoretic Approach By Jose de Jesus Herrera-Velasquez
  9. Equilibrium Behaviors in Reputation Games By Yingkai Li; Harry Pei
  10. Collusion in Two-Sided Markets By Yassine Lefouili; Joana Pinho
  11. Learning Utilities and Equilibria in Non-Truthful Auctions By Hu Fu; Tao Lin
  12. Off-Policy Exploitability-Evaluation and Equilibrium-Learning in Two-Player Zero-Sum Markov Games By Kenshi Abe; Yusuke Kaneko
  13. Inefficient Cooperation under Stochastic and Strategic Uncertainty By Lisa Bruttel; Werner Güth; Juri Nithammer; Andreas Orland
  14. Persuasion Bias in Science : An Experiment on Strategic Sample Selection By Arianna Degan; Ming Li; Huan Xie
  15. Violence amidst virus: A Game-theoretic exploration of conflict during a pandemic By Munshi, Soumyanetra
  16. Games with Unobservable Heterogeneity and Multiple Equilibria : An Application to Mobile Telecommunications By Mathieu Marcoux
  17. Optimally Stubborn By Anna Sanktjohanser
  18. Cooperation in a State of Anarchy By Muthoo, Abhinay

  1. By: Simon Hoof (Paderborn University)
    Abstract: We consider a n-person pure bargaining game in which the payoff space of feasible agreements is constructed via a noncooperative cake eating differential game. At the beginning of the game the agents bargain over strategies to be played during the game while the noncooperative Nash equilibrium serves as the disagreement strategies. An initial cooperative solution (a strategy tuple) is called time consistent if renegotiating it at a later time instant yields the original solution and subgame individually rational if it remains individually rational to stick to the initial solution throughout the game. We show that time consistent and subgame individually rational bargaining solutions exist if the space of cooperative strategies is restricted to linear functions and the bargaining solution is a maximizer of some linear homogenous function.
    Keywords: : cooperative NTU differential games, time consistency, bargaining solution
    JEL: C61 C71 C78
    Date: 2020–04
  2. By: Isaiah Farahbakhsh; Chrystopher L. Nehaniv
    Abstract: The prisoner's dilemma (PD) is a game-theoretic model studied in a wide array of fields to understand the emergence of cooperation between rational self-interested agents. In this work, we formulate a spatial iterated PD as a discrete-event dynamical system where agents play the game in each time-step and analyse it algebraically using Krohn-Rhodes algebraic automata theory using a computational implementation of the holonomy decomposition of transformation semigroups. In each iteration all players adopt the most profitable strategy in their immediate neighbourhood. Perturbations resetting the strategy of a given player provide additional generating events for the dynamics. Our initial study shows that the algebraic structure, including how natural subsystems comprising permutation groups acting on the spatial distributions of strategies, arise in certain parameter regimes for the pay-off matrix, and are absent for other parameter regimes. Differences in the number of group levels in the holonomy decomposition (an upper bound for Krohn-Rhodes complexity) are revealed as more pools of reversibility appear when the temptation to defect is at an intermediate level. Algebraic structure uncovered by this analysis can be interpreted to shed light on the dynamics of the spatial iterated PD.
    Date: 2020–07
  3. By: Din Cohen (BGU); Aner Sela (BGU)
    Keywords: Group contests, asymmetric information
    JEL: C72 D44 D82
    Date: 2020
  4. By: Ezra Einy (BGU); Diego Moreno (Departamento de Economia, Universidad Carlos III de Madrid); Aner Sela (BGU)
    Keywords: Tullock Contests, Incomplete Information, Robustness of Equilibria
    JEL: C72 D44 D82
    Date: 2020
  5. By: Ori Haimanko (BGU)
    Keywords: Generalized Tullock contests, Bayesian Nash Equilibrium, equi- librium existence, absolute continuity, information structures, continuum of types
    JEL: C72 D44 D82
    Date: 2020
  6. By: Victor Aguirregabiria (University of Toronto, CEPR); Mathieu Marcoux (Université de Montréal, CIREQ)
    Abstract: Imposing equilibrium restrictions provides substantial gains in the estimation of dynamic discrete games. Estimation algorithms imposing these restrictions – MPEC,NFXP, NPL, and variations – have different merits and limitations. MPEC guarantees local convergence, but requires the computation of high-dimensional Jacobians. The NPL algorithm avoids the computation of these matrices, but – in games – may fail to converge to the consistent NPL estimator. We study the asymptotic properties of the NPL algorithm treating the iterative procedure as performed in finite samples. We find that there are always samples for which the algorithm fails to converge, and this introduces a selection bias. We also propose a spectral algorithm to compute the NPL estimator. This algorithm satisfies local convergence and avoids the computation of Jacobian matrices. We present simulation evidence illustrating our theoretical results and the good properties of the spectral algorithm.
    JEL: C13 C57 C61 C73
    Date: 2019–09
  7. By: Chen Cohen (BGU); David Lagziel (BGU); Ofer Levi (BGU); Aner Sela (BGU)
    Keywords: All-pay contests, multiple prizes, complete information
    JEL: D44 D82 J31 J41
    Date: 2020
  8. By: Jose de Jesus Herrera-Velasquez (Graduate School of Economics, Kyoto University)
    Abstract: We develop a model of conglomerate mergers. There are two markets that are not related horizontally or vertically. Each market has an oligopoly structure where the firms compete in a Cournot fashion. The firms cannot merge with a firm in the same market, but they are able to with a firm in a different market. Without a merger, we assume that only the firms in one of the markets can invest in technology to reduce the cost of production. After the merger, the new formed conglomerate is able to use the technology in both markets. Using the technology has a cost of opportunity in the merger scenario, hence the conglomerate has to decide how to allocate the technology across both markets. The model predicts that in a monopoly benchmark, the incentives to allocate the technology are to reduce the costs in the markets with better prospects of prots. In an oligopoly structure, the firms merge if they have incentives to transfer the technology from the original market either to invest in the better markets or to avoid technological competition. We fully characterize how the markets' size and the technological compatibility determine the equilibrium market outcomes and the underlying merger decisions. We derive welfare implications of the equilibria.
    Keywords: Conglomerate Mergers; Corporate Diversication; Game Theory; Resources; Multimarket Competition
    Date: 2020–08
  9. By: Yingkai Li; Harry Pei
    Abstract: We examine a patient player's behavior when he can build a reputation in front of a sequence of myopic opponents. With positive probability, the patient player is a commitment type who mechanically plays his Stackelberg action in every period. We characterize the patient player's action frequencies in equilibrium. Our results clarify the extent to which reputation effects can refine the patient player's equilibrium behavior.
    Date: 2020–07
  10. By: Yassine Lefouili; Joana Pinho
    Abstract: This paper explores the incentives for, and the effects of, collusion in prices between two-sided platforms. We characterize the most profitable sustainable agreement when platforms collude on both sides of the market and when they collude on a single side of the market. Under two-sided collusion, prices on both sides are higher than the competitive prices, implying that agents on both sides become worse off as compared to the competitive outcome. An increase in cross-group externalities makes two-sided collusion harder to sustain, and reduces the harm from collusion suffered by the agents on a given side as long as the collusive price on that side is lower than the monopoly price. When platforms collude on a single side of the market, the price on the collusive side is lower (higher) than the competitive price if the magnitude of the cross-group externalities exerted on that side is sufficiently large (small). As a result, one-sided collusion may benefit the agents on the collusive side and harm the agents on the competitive side.
    Keywords: Collusion; Two-sided markets; Cross-group externalities
    JEL: L41 D43
    Date: 2020–04
  11. By: Hu Fu; Tao Lin
    Abstract: In non-truthful auctions, agents' utility for a strategy depends on the strategies of the opponents and also the prior distribution over their private types; the set of Bayes Nash equilibria generally has an intricate dependence on the prior. Using the First Price Auction as our main demonstrating example, we show that $\tilde O(n / \epsilon^2)$ samples from the prior with $n$ agents suffice for an algorithm to learn the interim utilities for all monotone bidding strategies. As a consequence, this number of samples suffice for learning all approximate equilibria. We give almost matching (up to polylog factors) lower bound on the sample complexity for learning utilities. We also consider settings where agents must pay a search cost to discover their own types. Drawing on a connection between this setting and the first price auction, discovered recently by Kleinberg et al. (2016), we show that $\tilde O(n / \epsilon^2)$ samples suffice for utilities and equilibria to be estimated in a near welfare-optimal descending auction in this setting. En route, we improve the sample complexity bound, recently obtained by Guo et al. (2019), for the Pandora's Box problem, which is a classical model for sequential consumer search.
    Date: 2020–07
  12. By: Kenshi Abe; Yusuke Kaneko
    Abstract: Off-policy evaluation (OPE) is the problem of evaluating new policies using historical data obtained from a different policy. Off-policy learning (OPL), on the other hand, is the problem of finding an optimal policy using historical data. In recent OPE and OPL contexts, most of the studies have focused on one-player cases, and not on more than two-player cases. In this study, we propose methods for OPE and OPL in two-player zero-sum Markov games. For OPE, we estimate exploitability that is often used as a metric for determining how close a strategy profile is to a Nash equilibrium in two-player zero-sum games. For OPL, we calculate maximin policies as Nash equilibrium strategies over the historical data. We prove the exploitability estimation error bounds for OPE and regret bounds for OPL based on the doubly robust and double reinforcement learning estimators. Finally, we demonstrate the effectiveness and performance of the proposed methods through experiments.
    Date: 2020–07
  13. By: Lisa Bruttel (University of Potsdam); Werner Güth (LUISS Guido Carli, Max Planck Institute for Research on Collective Goods); Juri Nithammer (University of Potsdam); Andreas Orland (University of Potsdam)
    Abstract: Stochastic uncertainty can cause difficult coordination problems that may hinder mutually beneficial cooperation. We propose a mechanism of ex-post voluntary transfers designed to circumvent these coordination problems and ask whether it can do so. To test this, we implement a controlled laboratory experiment based on a repeatedly played Ultimatum Game with a stochastic endowment. Contrary to our hypothesis, we find that allowing voluntary transfers does not entail an efficiency increase. We suggest and analyze two main reasons for this finding: First, the stochastic uncertainty forces proposers to accept high strategic uncertainty if they intend to cooperate by claiming a low amount (which many proposers do not). Second, many responders behave only incompletely conditionally cooperative by transferring too little (which hinders cooperation in future periods).
    Keywords: stochastic uncertainty, strategic uncertainty, cooperation, Ultimatum Game, experiment
    JEL: C78 C92 D74
    Date: 2020–09
  14. By: Arianna Degan (UQAM and CDER); Ming Li (Concordia University, CIRANO and CIREQ); Huan Xie (Concordia University, CIRANO and CIREQ)
    Abstract: We experimentally test a game theoretical model of researcher-evaluator interaction à la Di Tillio, Ottaviani, and Sørensen (2017a). Researcher may strategically manipulate sample selection using his private information in order to achieve favourable research outcomes and thereby obtain approval from Evaluator. Our experimental results confirm the theoretical predictions for Researcher’s behaviour but find significant deviations from them about Evaluator’s behaviour. However, comparative statics are mostly consistent with the theoretical predictions. In the welfare analysis, we find that Researcher always benefits from the possibility of manipulation, in contrast to the theoretical prediction that he some-times is hurt by it. Consistent with theoretical predictions, Evaluator benefits from the possibility of Researcher’s manipulation when she leans towards approval or is approximately neutral but is hurt by that possibility when she leans against approval.
    Keywords: persuasion bias, research conduct, manipulation, sample selection, experiment, randomized controlled trials
    JEL: C72 C92 D83
    Date: 2019–11
  15. By: Munshi, Soumyanetra
    Abstract: This paper explores how the COVID-19 pandemic is affecting conflicts world-wide. On one hand, confrontation would expose both states and violent non-state groups to contamination, potentially causing massive loss of human lives. Moreover, attacks aimed at signalling discontent or making bigger demands, are unlikely to generate media and diplomatic attention at the level it otherwise would have, sans the pandemic. Hence there might be a mitigation in the intensity of conflicts. On the other hand, the capacity of the states to retaliate will, to a large extent, be compromised, since huge financial and human resources will have to be dedicated to fighting the widespread health and economic effects of the pandemic. Hence the belligerent groups may have greater incentive to launch attacks. This paper attempts to game-theoretically study these various issues and incentives facing the conflicting parties, under the threat of COVID-19. We consider the simple conflict model by Hirshleifer and augment it by introducing possible effects that a raging pandemic might impose on the conflicting parties. Specifically, we introduce positive and negative externalities that a pandemic may impose on an existing conflict and explore parametric conditions under which it is likely to aggravate or mitigate. We find that conflicts are generally likely to lessen but may increase under specific circumstances. We present some narrative evidence on how conflicts seem to have ameliorated in a pandemic-stricken world.
    Keywords: violence under pandemic, conflict under pandemic, conflict with externalities
    JEL: C72 D74
    Date: 2020–08–19
  16. By: Mathieu Marcoux (Université de Montréal, CIREQ)
    Abstract: To shed light on the limited success of competition enhancing policies in mobile telecommunications, I estimate a game of transceivers’ locations between national incumbents and a new entrant in Canada. I recover player-specific unobserved heterogeneity from bids for spectrum licenses to address the unavailability of regressors required to identify incumbents’ responses to the new entrant’s decisions. I find that incumbents benefitting from important economies of density is a plausible explanation for policies’ drawbacks. I then evaluate the equilibrium effect of subsidizing the new entrant’s transceivers and find that this alternative proposition increases its investments while only slightly modifying incumbents.
    Keywords: multiple equilibria, unobserved heterogeneity, empirical games, telecommunications
    JEL: C57 L11
    Date: 2019–02
  17. By: Anna Sanktjohanser (Cowles Foundation, Yale University)
    Abstract: I consider a bargaining game with two types of players – rational and stubborn. Rational players choose demands at each point in time. Stubborn players are restricted to choose from the set of “insistent†strategies that always make the same demand and never accept anything less. However, their initial choice of demand is unrestricted. I characterize the equilibria of this game. I show that while pooling equilibria exist, fully separating equilibria do not. Relative to the case with exogenous behavioral types, strong behavioral predictions emerge: in the limit, players randomize over at most two demands. However, unlike in a world with exogenous types, there is Folk-theorem-like payoff multiplicity.
    Keywords: Reputation, Bargaining, Behavioral types, War of attrition
    Date: 2020–08
  18. By: Muthoo, Abhinay (University of Warwick)
    Abstract: We lay down a simple (game-theoretic) model of a state-of-anarchy involving three players. We focus attention on the following question : Which subset of players (if any) will agree to cooperate amongst each other? Will all three players agree to do so, or only two of the three players (and if so, which two players)? Or will no player agree to cooperate with any other player? We show that the socially optimal outcome is for all three players to agree to cooperate with each other. We also show that due to the presence of positive externalities, in equilibrium, cooperation may only be established between two of the three players (which is sub-optimal). JEL codes: D62 ; D74 ; F02
    Date: 2020

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