nep-gth New Economics Papers
on Game Theory
Issue of 2018‒07‒30
seventeen papers chosen by
Sylvain Béal
Université de Franche-Comté

  1. The Big Robber Game By Carlos Alós-Ferrer; Jaume García-Segarra; Alexander Ritschel
  2. Two classes of weighted values for coalition structures with extensions to level structures By Besner, Manfred
  3. Asymptotic value in frequency-dependent games: A differential approach By Joseph Abdou; Nikolaos Pnevmatikos
  4. Cultural values and behavior in dictator, ultimatum and trust games: an experimental study By Sun-Ki Chai; Dolgorsuren Dorj; Katerina Sherstyuk
  5. A Theory of Auctions with Endogenous Valuations By Benny Moldovanu; Alex Gershkov; Philipp Strack
  6. Majoritarian aggregation and Nash implementation of experts' opinions By Pablo Amorós
  7. Skewed Information Transmission By Francesc Dilmé
  8. The Heaven Dictator Game: Costless taking or giving By Aurora García-Gallego; Nikolaos Georgantzis; María José Ruiz-Martos
  9. "Timing Games with Irrational Types: Leverage-Driven Bubbles and Crash-Contingent Claims" By Hitoshi Matsushima
  10. "Stochastic Differential Game in High Frequency Market" By Taiga Saito; Akihiko Takahashi
  11. On Interactive Sequencing Situations with Exponential Cost Functions By Saavedra-Nieves, Alejandro; Schouten, Jop; Borm, Peter
  12. Managing Competition on a Two-Sided Platform By Paul Belleflamme; Martin Peitz
  13. Replication in experimental economics: A historical and quantitative approach focused on public good game experiments By Nicolas Vallois; Dorian Jullien
  14. Conflict Over Transnational River Resources: An Applied Game Theoretic Analysis By Andrew Beckmann
  15. 'Discrete beliefs space and equilibrium: a cautionary note' By Michele Berardi
  16. On the iterated estimation of dynamic discrete choice games By Federico A. Bugni; Jackson Bunting
  17. Quantity-cum-Quality Contests By J. Atsu Amegashie

  1. By: Carlos Alós-Ferrer; Jaume García-Segarra; Alexander Ritschel
    Abstract: We present a novel design measuring a correlate of social preferences in a high-stakes setting. In the Big Robber Game, a "robber" can obtain large personal gains by appropriating the gains of a large group of "victims" as seen in recent corporate scandals. We observed that more than half of all robbers take as much as possible. At the same time, participants displayed standard, prosocial behavior in the Dictator, Ultimatum, and Trust games. That is, prosocial behavior in the small is compatible with highly selfish actions in the large, and the essence of corporate scandals can be reproduced in the laboratory even with a standard student sample. We show that this apparent contradiction is actually consistent with received social-preference models. In agreement with this view, in the experiment more selfish robbers also behaved more selfishly in other games and in a donation question. We conclude that social preferences are compatible with rampant selfishness in high-impact decisions affecting a large group.
    Keywords: Big Robber Game, social preferences, corporate scandals, incentives
    JEL: C72 C92 D03
    Date: 2018–06
  2. By: Besner, Manfred
    Abstract: In this paper we introduce two new classes of weighted values for coalition structures with related extensions to level structures. The values of both classes coincide on given player sets with Harsanyi payoffs and match therefore adapted standard axioms for TU-values which are satisfied by these values. Characterizing elements of the values from the new classes are a new weighted proportionality within components property and a null player out property, but on different reduced games for each class. The values from the first class, we call them weighted Shapley alliance coalition structure values (weighted Shapley alliance levels values), satisfy the null player out property on usual reduced games. By contrast, the values from the second class, named as weighted Shapley collaboration coalition structure values (weighted Shapley collaboration levels values) have this property on new reduced games where a component decomposes in components of lower levels (these are singletons in a coalition structure) if one player of this component is removed from the game. The first class contains the Owen value (Shapley levels value) and the second class includes a new extension of the Shapley value to coalition structures (level structures) as a special case.
    Keywords: Cooperative game · Weighted Shapley coalition structure values · Weighted Shapley levels values · Weighted proportionality within components · Dividends
    JEL: C70 C71
    Date: 2018–07–04
  3. By: Joseph Abdou (Centre d'Economie de la Sorbonne); Nikolaos Pnevmatikos (Université Paris 2 Panthéon-Assas)
    Abstract: We study the asymptotic value of a frequency-dependent zero-sum game following a differential approach. In such a game the stage payoffs depend on the current action and on the frequency of actions played so far. We associate in a natural way a differential game to the original game and although it presents an irregularity at the origin, we prove existence of the value on the time interval [0,1]. We conclude, using appropriate approximations, that the limit of Vn, as n tends to infinity exists and coincides with the value of the associated continuous time game. We extend the existence of the asymptotic value to discounted payoffs and we show that V? as ? tends 0, converges to the same limit
    Keywords: stochastic game; frequency dependent payoffs; continuous-time game; Hamilton-Jacobi-Bellman-Isaacs equation
    JEL: C73
    Date: 2016–11
  4. By: Sun-Ki Chai (Department of Sociology, University of Hawaii at Manoa); Dolgorsuren Dorj (Department of Economics, National Academy of Governance); Katerina Sherstyuk (Department of Economics, University of Hawaii at Manoa)
    Abstract: Culture is a central concept broadly studied in social anthropology and sociology. It has been gaining increasing attention in economics in relation to research on discrimination in a labor market, identity, gender, and social preferences. Most experimental economics research on culture studies cross-national or cross-ethnic differences in economic behavior. These studies reveal clear behavioral differences across different ethnic groups, yet do not provide a general deductive framework for specifying the underlying preferences behind these differences. We explain laboratory behavior in the dictator, ultimatum, and trust games based on two cultural dimensions adopted from a prominent general cultural framework in contemporary social anthropology: group commitment and grid control. Group-ness measures the extent to which individual identity is incorporated into group or collective identity; grid-ness measures the extent to which social and political prescriptions intrinsically influence individual behavior. One objective of this paper is to show that the grid-group framework, despite its origins in comparative ethnography, is adaptable to an experimental setting and indeed provides a parsimonious framework for generating testable behavioral predictions across a variety of experimental games. Another is to test the predictions of the grid- group framework on a number of simple games widely employed by experimental economists. Grid-group characteristics are measured for each individual using selected items from the World Values Survey. We find that these attributes allow us to systematically predict behavior in a way that discriminates among multiple forms of social preferences using a simple, parsimonious deductive model. Based on the implications of the theory, we hypothesize that subjects with higher group scores will tend to offer more in dictator and ultimatum games and entrust more in trust games. When responding in ultimatum games, those with high grid scores are hypothesized to reject more often and divide less, and to tie acceptance and amount divided more closely to the amount offered. When responding in trust games, those with low group scores are hypothesized to return less, and those with high grid scores to tie the amount returned more closely to the amount entrusted. These theoretical predictions are confirmed overall for most experimental games, although the strength of empirical support varies across games. We conclude that grid-group cultural theory is a viable predictor of people’s economic behavior, and further discuss potential limitations of the current approach and the ways to improve it.
    Keywords: laboratory experiment, two-person games, survey, culture
    JEL: C72 C91 Z13
    Date: 2018–05
  5. By: Benny Moldovanu; Alex Gershkov; Philipp Strack
    Abstract: We study the revenue maximizing allocation of m units among n symmetric agents that have unit demand and convex preferences over the probability of receiving an object. Such preferences are naturally induced by a game where the agents take costly actions that affect their values before participating in the mechanism. Both the uniform m + 1 price auction and the discriminatory pay-your-bid auction with reserve prices constitute symmetric revenue maximizing mechanisms. Contrasting the case with linear preferences, the optimal reserve price reacts to both demand and supply, i.e., it depends both on the number of objects m and on number of agents n. The main tool in our analysis is an integral inequality involving majorization, super-modularity and convexity due to Fan and Lorentz (1954).
    Keywords: revenue maximization, endogenous values , investments, majorization
    JEL: D44
    Date: 2018–07
  6. By: Pablo Amorós (Department of Economics, University of Málaga)
    Abstract: A group of experts must choose the winner of a competition. The honest opinions of the experts must be aggregated to determine the deserving winner. The aggregation rule is majoritarian if it respects the honest opinion of the majority of experts. An expert might not want to reveal her honest opinion if, by doing so, a contestant that she likes more is chosen. Then, we have to design a mechanism that implements the aggregation rule. We show that, in general, no majoritarian aggregation rule is Nash implementable, even if no expert has friends or enemies among the contestants.
    Keywords: mechanism design; Nash equilibrium; aggregation of experts' opinions; jury
    JEL: C72 D71 D78
    Date: 2018–07
  7. By: Francesc Dilmé
    Abstract: This paper analyzes strategic information transition between skewed agents. More concretely, we study the Crawford and Sobel (1982) setting in the case where agents are not biased, but they differ on the relative importance they put on avoiding "upward" or "downward" mistakes. We show that, even though the agents could fully communicate when the state of the world was perfectly observed by the sender, the information transmission is significantly imprecise in any equilibrium when there is a small noise in the observation. Hence, contrary to what was previous thought, a low objective misalignment is not sufficient for precise equilibrium communication.
    Keywords: Strategic Communication, Skewed Preferences
    JEL: C72 D82 D83
    Date: 2018–07
  8. By: Aurora García-Gallego (LEE & Economics Department, Universitat Jaume I, Castellón-Spain); Nikolaos Georgantzis (Burgundy School of Wines and Spirits Business, Dijon, France); María José Ruiz-Martos (Dept. de Teoría e Historia Económica, University of Granada, Spain)
    Abstract: We present experimental data from the Heaven-Dictator game, a generalization of the dictator game that investigates the overstatement of inequality reduction in the motivation of social preferences. In this game, two players start with equal endowments and the heaven-dictator player, without incurring in any pecuniary cost or profit, chooses among increasing, decreasing or maintaining the earnings of the passive player. Thus, any choice except for the status quo generates unequal payoffs. The design avoids the experimenter demand effect of the standard “give only” version while simultaneously allowing participants to manifest antisocial preferences, inequity aversion or retaliation cannot be called for as motives. We find that the overwhelming majority of subjects, 75.4%, choose to increase their partners’ earnings; however, there is a non-negligible 24.6% of subjects that either choose the status quo (11.9%) or to decrease (12.7%) their partners’ earnings. Based on the psychological literature on music as a mood-inducing stimulus and on the effects of mood on helping behavior, we study the effect of exposure to different types of music on the heaven-dictator choices. Overall, observed preferences are independent of the music condition.
    Keywords: experiment, behavior, other-regarding preferences, music, dictator game
    JEL: C72 C91
    Date: 2018
  9. By: Hitoshi Matsushima (Faculty of Economics, The University of Tokyo)
    Abstract: This study investigates a timing game with irrational types; each player selects a time in a fixed time interval, and the player who selects the earliest time wins the game. We assume the possibility of irrational types in that each player is irrational with a positive probability, thus selecting the terminal time. We show that there exists the unique Nash equilibrium; according to it, every player never selects the initial time. As an application, we analyze a strategic aspect of leverage-driven bubbles; even if a company is unproductive, its stock price grows up according to an exogenous reinforcement pattern. During the bubble, this company is willing to raise huge funds by issuing new shares. We regard players as arbitrageurs, who decide whether to ride the bubble or burst it. We demonstrate two models, which are distinguished by whether crash-contingent claim, i.e., contractual agreement such that the purchaser of this claim receives a promised monetary amount from its seller if and only if the bubble crashes, is available. The availability of this claim deters the bubble; without crash-contingent claim, the bubble emerges and persists even if the degree of reinforcement is insufficient. Without crash-contingent claim, high leverage ratio fosters the bubble, while with crash-contingent claim, it rather deters the bubble.
    Date: 2018–06
  10. By: Taiga Saito (CIRJE, Faculty of Economics, The University of Tokyo); Akihiko Takahashi (CIRJE, Faculty of Economics, The University of Tokyo)
    Abstract: This paper presents an application of a linear quadratic stochastic differential game to a model in finance, which describes trading behaviors of different types of players in a high frequency stock market. Stability of the high frequency market is a central issue for financial markets. Building a model that expresses the trading behaviors of the different types of players and the price actions in turmoil is important to set regulations to maintain fair markets. Firstly, we represent trading behaviors of the three types of players, algorithmic traders, general traders, and market makers as well as the mid-price process of a risky asset by a linear quadratic stochastic differential game. Secondly, we obtain a Nash equilibrium for open loop admissible strategies by solving a forward-backward stochastic differential equation (FBSDE) derived from the stochastic maximum principle. Finally, we present numerical examples of the Nash equilibrium for open loop admissible strategies and the corresponding price action of the risky asset, which agree with the empirical findings on trading behaviors of players in high frequency markets. This model can be used to investigate the impact of regulation changes on the market stability as well as trading strategies of the players.
    Date: 2018–05
  11. By: Saavedra-Nieves, Alejandro; Schouten, Jop (Tilburg University, Center For Economic Research); Borm, Peter (Tilburg University, Center For Economic Research)
    Abstract: This paper addresses interactive one-machine sequencing situations in which the costs of processing a job are given by an exponential function of its completion time. The main difference with the standard linear case is that the gain of switching two neighbors in a queue is time-dependent and depends on their exact position. We illustrate that finding an optimal order is complicated in general and we identify specific subclasses, which are tractable from an optimization perspective. More specifically, we show that in these subclasses, all neighbor switches in any path from the initial order to an optimal order lead to a non-negative gain. Moreover, we derive conditions on the time-dependent neighbor switching gains in a general interactive sequencing situation to guarantee convexity of the corresponding cooperative game. These conditions are satisfied within our specific subclasses of exponential interactive sequencing situations.
    Keywords: interactive sequencing situation; initial order; exponential cost function; sequencing games; convexity
    JEL: C44 C71
    Date: 2018
  12. By: Paul Belleflamme; Martin Peitz
    Abstract: On many two-sided platforms, users on one side not only care about user participation and usage levels on the other side, but they also care about participation and usage of fellow users on the same side. Most prominent is the degree of seller competition on a platform catering to buyers and sellers. In this paper, we address how seller competition affects platform pricing, product variety, and the number of platforms that carry trade.
    Keywords: Network effects, two-sided markets, platform competition, intermediation, pricing, imperfect competition
    JEL: D43 L13 L86
    Date: 2018–07
  13. By: Nicolas Vallois (CES - Centre d'économie de la Sorbonne - UP1 - Université Panthéon-Sorbonne - CNRS - Centre National de la Recherche Scientifique); Dorian Jullien (GREDEG - Groupe de Recherche en Droit, Economie et Gestion - UNS - Université Nice Sophia Antipolis - UCA - Université Côte d'Azur - CNRS - Centre National de la Recherche Scientifique)
    Abstract: We propose a historical perspective on replication in experimental economics focused on public good games. Our intended contribution is twofold: in terms of method and in terms of object. Methodologically, we blend traditional qualitative history of economics with a less traditional quantitative approach using basic econometric tools to detect unnoticed historical patterns of replication. In terms of our object, we highlight a type of replication that we call " baseline replication " , which is not present in explicit methodological discussions, yet central in the specificity of experimental economics regarding replication in economics.
    Keywords: Experimental Economics, Replication, History of Economic Thought,Methodology, Public Good Experiments
    Date: 2017–11–28
  14. By: Andrew Beckmann (University of Hawai’i and the East West Center)
    Abstract: This paper presents a game theoretic model to analyze transnational river resource conflicts such as the Indus River Basin conflict between Pakistan and India. The model demonstrates that to obtain a share of the river resources from the upstream country downstream, the downstream country must purchase costly armaments to threaten an invasion. Yet in this process, the upstream country has a significant first-mover advantage in extracting the river resource as it can internalize the threat of invasion and prevent it from happening in the non-invasion equilibrium ``Peace with Threat of War†. When the upstream country does not internalize the threat of invasion from the downstream country, the invasion equilibrium ``War†occurs. This paper discusses the implications of each equilibria in the model within the context of the Indus River Basin conflict. This paper also discusses the possibility of Pareto-improving cooperative outcomes by imposing new institutional frameworks.
    Keywords: India, Indus River Basin, International Conflict, Pakistan, Third-Party Arbitration, Transnational River
    JEL: F51 F55
    Date: 2018–05
  15. By: Michele Berardi
    Abstract: Bounded rationality requires assumptions about ways in which rationality is constrained and agents form their expectations. Evolutionary schemes have been used to model beliefs dynamics, with agents choosing endogenously among a limited number of beliefs heuristics according to their relative performance. This work shows that arbitrarily constraining the beliefs space to a ?nite (small) set of possibilities can generate arti?cial equilibria that can be stable under evolutionary dynamics. Only when "enough" heuristics are available, beliefs in equilibrium are not arti?cially constrained. I discuss these ?ndings in light of an alternative approach to modelling beliefs dynamics, namely adaptive learning.
    Date: 2018
  16. By: Federico A. Bugni (Institute for Fiscal Studies and Duke University); Jackson Bunting (Institute for Fiscal Studies)
    Abstract: We study the asymptotic properties of a class of estimators of the structural parameters in dynamic discrete choice games. We consider K-stage policy iteration (PI) estimators, where K denotes the number of policy iterations employed in the estimation. This class nests several estimators proposed in the literature. By considering a "maximum likelihood" criterion function, our estimator becomes the K- ML estimator in Aguirregabiria and Mira (2002, 2007). By considering a "minimum distance" criterion function, it de nes a new K-MD estimator, which is an iterative version of the estimators in Pesendorfer and Schmidt-Dengler (2008) and Pakes et al. (2007). First, we establish that the K-ML estimator is consistent and asymptotically normal for any K. This complements ndings in Aguirregabiria and Mira (2007), who focus on K = 1 and K large enough to induce convergence of the estimator. Furthermore, we show that the asymptotic variance of the K-ML estimator can exhibit arbitrary patterns as a function K. Second, we establish that the K-MD estimator is consistent and asymptotically normal for any K. For a specifi c weight matrix, the K-MD estimator has the same asymptotic distribution as the K-ML estimator. Our main result provides an optimal sequence of weight matrices for the K-MD estimator and shows that the optimally weighted K-MD estimator has an asymptotic distribution that is invariant to K. This new result is especially unexpected given the findings in Aguirregabiria and Mira (2007) for K-ML estimators. Our main result implies two new and important corollaries about the optimal 1-MD estimator (derived by Pesendorfer and Schmidt-Dengler (2008)). First, the optimal 1-MD estimator is optimal in the class of K-MD estimators for all K. In other words, additional policy iterations do not provide asymptotic efficiency gains relative to the optimal 1-MD estimator. Second, the optimal 1-MD estimator is more or equally asymptotically efficient than any K-ML estimator for all K.
    Keywords: dynamic discrete choice problems, dynamic games, pseudo maximum likelihood estimator, minimum distance estimator, estimation, asymptotic efficiency
    JEL: C13 C61 C73
    Date: 2018–02–16
  17. By: J. Atsu Amegashie
    Abstract: I consider a contest in which the quantity of output is rewarded and another in which the quality of output is rewarded. The output in the quality contest plays a dual role. It counts in the quality contest but it is also converted into quantity-equivalent output to obtain total output in the quantity contest. This latter feature implies that the two contests are interlinked. Examples abound. There are contests in which there is a prize for the number (quantity) of publications by a scholar, a politician’s accomplishments, an athlete’s number of Olympic medals, etc and there is also a prize for a scholar’s publications in top journals, a politician's major accomplishments, or an athlete’s number of Olympic gold medals . I find that when the unit cost of producing quality is sufficiently high, then treating quality and quantity as the same has a disincentive effect on the production of quality. In contrast, when the unit cost of producing quality is sufficiently low, treating quality and quantity as the same has no disincentive effect on the production of quality. There is an equilibrium in which high-ability and low-ability contestants, in spite of being non-identical, have the same probability of winning the quantity contest. When contestants are budget-constrained, I find that whether an increase in the budget will increase effort in the quality contest depends on the size of the initial budget.
    Keywords: Bayesian Nash equilibrium, contests, quality, quantity
    JEL: D72
    Date: 2018

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