nep-gth New Economics Papers
on Game Theory
Issue of 2014‒04‒18
ten papers chosen by
Laszlo A. Koczy
Hungarian Academy of Sciences and Obuda University

  1. A Concise Axiomatization of a Shapley-type Value for Stochastic Coalition Processes By Ulrich Faigle; Michel Grabisch
  2. Equilibrium Selection in Sequential Games with Imperfect Information By Jon X. Eguia; Aniol Llorente-Saguer; Rebecca Morton; Antonio Nicolò
  3. Cost of Inequality, the Uniform Rule and Cooperative Games By Arsen Palestini; Giuseppe Pignataro
  4. Linear Transforms, Values and Least Square Approximation for Cooperation Systems By Ulrich Faigle; Michel Grabisch
  5. Observing the Strategies Subjects Identify from Choice Data in a Repeated Prisoner's Dilemma By Tobie Cusson; Jim Engle-Warnick
  6. On equilibrium payoffs in wage bargaining with discount rates varying in time By Ahmet Ozkardas; Agnieszka Rusinowska
  7. Insensitivity to Prices in a Dictator Game By Jim Engle-Warnick; Natalia Mishagina
  8. On Markov perfect equilibria in baseball By Akifumi Kira; Keisuke Inakawa
  9. Household Consumption When the Marriage is Stable By Laurens Cherchye; Thomas Demuynck; Bram De Rock; Frederic Vermeulen
  10. Responsabilité sociale d'une entreprise publique : une formalisation du jeu des acteurs By Myriam Donsimoni; Daniel Labaronne

  1. By: Ulrich Faigle (Universität zu Köln - Mathematisches Institut); Michel Grabisch (CES - Centre d'économie de la Sorbonne - CNRS : UMR8174 - Université Paris 1 - Panthéon-Sorbonne, EEP-PSE - Ecole d'Économie de Paris - Paris School of Economics - Ecole d'Économie de Paris)
    Abstract: The classical Shapley value is the average marginal contribution of a player, taken over all possible ways to form the grand coalition $N$ when one starts from the empty coalition and adds players one by one. In a previous paper, the authors have introduced an allocation scheme for a general coalition formation model where the evolution of the coalition of active players is ruled by a Markov chain and need not finish with the grand coalition. This note provides an axiomatization which is only slightly weaker than the original one but allows a much more transparent proof. Moreover, the logical independence of the axioms is exhibited.
    Keywords: Coalitional game; coalition formation process; Shapley value
    Date: 2013
  2. By: Jon X. Eguia (University of Bristol); Aniol Llorente-Saguer (Queen Mary University of London); Rebecca Morton (New York University); Antonio Nicolò (University of Manchester)
    Abstract: Games with imperfect information often feature multiple equilibria, which depend on beliefs off the equilibrium path. Standard selection criteria such as passive beliefs, symmetric beliefs or wary beliefs rest on ad hoc restrictions on beliefs. We propose a new selection criterion that imposes no restrictions on beliefs: we select the action profile that is supported in equilibrium by the largest set of beliefs. We conduct experiments to test the predictive power of the existing and our novel selection criteria in two applications: a game of vertical multi-lateral contracting, and a game of electoral competition. We find that our selection criterion outperforms the other selection criteria.
    Keywords: Equilibrium selection, Passive beliefs, Symmetric beliefs, Vertical contracting, Multiple equilibria, Imperfect information
    JEL: C72 D86 H41 D72
    Date: 2014–04
  3. By: Arsen Palestini (MEMOTEF, Sapienza University of Rome, Via del Castro Laurenziano 9, 00161 Rome, Italy.); Giuseppe Pignataro (Department of Economics, University of Bologna, Strada Maggiore 45, 40125 Bologna, Italy.)
    Abstract: The assessment of income inequality can be investigated looking at the solution concepts of the cooperative game theory. We propose a multi-factorial decomposition of the Atkinson index by income sources and evaluate it as a cooperative game of the social cost of inequality. This framework extends the distributive and efficient properties of the uniform rule (Sprumont [35]) in a setup with heterogeneous income sources and single-peaked preferences. We provide an axiomatic foundation of this preference-based allocation rule, called weakly uniform rule, with a further comparison with the solution concept of nucleolus. Sufficient conditions for their coincidence are therefore defined. Finally we characterize a welfare loss game expressed as the difference between the sum of inequalities generated by each source and the cost of the entire distribution. We show that income factors' contributions may increase or decrease the income inequality in the society ensuring different perspectives in terms of public policies.
    Keywords: Atkinson index, cost game, uniform rule, income sources, single-peaked preferences.
    JEL: C71 D33 D63 D71 I32
    Date: 2014–02
  4. By: Ulrich Faigle (Universität zu Köln - Mathematisches Institut); Michel Grabisch (CES - Centre d'économie de la Sorbonne - CNRS : UMR8174 - Université Paris 1 - Panthéon-Sorbonne, EEP-PSE - Ecole d'Économie de Paris - Paris School of Economics - Ecole d'Économie de Paris)
    Abstract: We study linear properties of TU-games, revisiting well-known issues like interaction transforms, the inverse Shapley value problem and the concept of semivalues and least square values. We embed TU-games into the model of cooperation systems and influence patterns, which allows us to introduce linear operators on games in a natural way. We focus on transforms, which are linear invertible maps, relate them to bases and investigate many examples (Möbius transform, interaction transform, walsh transform, etc.). In particular, we present a simple solution to the inverse problem in its general form: Given a linear value Φ and a game v, find all games v′ such that Φ(v) = Φ(v′). Generalizing Hart and Mas-Colell's concept of a potential, we introduce general potentials and show that every linear value is induced by an appropriate potential. We furthermore develop a general theory of allocations with a quadratic optimality criterion under linear constraints, obtaining results of Charnes et al., and Ruiz et al., and others as special cases. We prove that this class of allocations coincides exactly with the class of all linear values.
    Keywords: Cooperation system; cooperative game; basis; transform; inverse problem; potential; linear value; semivalue
    Date: 2014–01
  5. By: Tobie Cusson; Jim Engle-Warnick
    Abstract: We experimentally test the ability of subjects to identify repeated-game strategies from prisoner's dilemma choice data. In the experiments, subjects use a finite state grammar to build models to fit game histories. The histories are designed to distinguish between strategies with empirical and theoretical validity. We find that subjects successfully identify unconditional, punishment, and counting strategies. When data are observationally equivalent among different strategies, punishment strategies tend to be inferred. When inferred strategies do not fit the data, they tend to be more complex than necessary and to contain positive reciprocity and forgiveness. Our experiment provides an empirical basis for repeated-game strategies and sheds new light on play in repeated games.
    Keywords: Repeated game, prisoner's dilemma, finite automata, strategies,
    JEL: C90 C73 D03
    Date: 2013–08–01
  6. By: Ahmet Ozkardas (CES - Centre d'économie de la Sorbonne - CNRS : UMR8174 - Université Paris 1 - Panthéon-Sorbonne); Agnieszka Rusinowska (CES - Centre d'économie de la Sorbonne - CNRS : UMR8174 - Université Paris 1 - Panthéon-Sorbonne)
    Abstract: We provide an equilibrium analysis of a wage bargaining model between a union and a firm in which the union must choose between strike and holdout in case of a disagreement. While in the literature it is assumed that the parties of wage bargaining have constant discount factors, in our model preferences of the union and the firm are expressed by sequences of discount rates varying in time. First, we describe necessary conditions under arbitrary sequences of discount rates for the supremum of the union's payoffs and the infimum of the firm's payoffs under subgame perfect equilibrium in all periods when the given party makes an offer. Then, we determine the equilibrium payoffs for particular cases of sequences of discount rates varying in time. Besides deriving the exact bounds of equilibrium payoffs, we also characterize the equilibrium strategy profiles that support these extreme payoffs.
    Keywords: Union; firm bargaining; varying discount rates; subgame perfect equilibrium; equilibrium payoffs
    Date: 2014–02
  7. By: Jim Engle-Warnick; Natalia Mishagina
    Abstract: We show that violations of demand theory are more numerous than previously reported in experimental two-player dictator games. We then apply a new procedure consisting of income-compensated price adjustments that makes the choice sets rationalizable. We introduce a “weighted price” function that shows that violations of revealed preference can be interpreted as the dictator's insensitivity to the price of the dictator's allocation relative to the responder's allocation. Our paper is the first to rationalize violations of demand theory in dictator games by examining the relationship between violations of GARP and prices. We suggest that weighted prices, and not only preferences, may be a component of decision making in dictator games
    Keywords: Dictator Game, WARP, Revealed Preference,
    Date: 2014–02–01
  8. By: Akifumi Kira; Keisuke Inakawa
    Abstract: We formulate baseball as a finite Markov game with approximately 3.5 million states. The manager of each opposing team is the player who maximizes the probability of their team winning. We derive, using dynamic programming, a recursive formula which is satisfied by Markov perfect equilibria and the value functions of the game for both teams. By solving this recursive formula, we can obtain optimal strategies for each condition. We demonstrate with numerical experiments that these can be calculated in approximately 1 second per game.
    Date: 2014–03
  9. By: Laurens Cherchye; Thomas Demuynck; Bram De Rock; Frederic Vermeulen
    Abstract: We develop a novel framework to analyze the structural implications of the marriage market for house-hold consumption patterns. We start by de…ning a revealed preference characterization of e¢ cient householdconsumption when the marriage is stable. In particular, stability means that the marriage matching is indi-vidually rational and has no blocking pairs. We show that this revealed preference characterization generatestestable conditions even if there is only a single consumption observation per household and individual pref-erences are heterogeneous across households. In addition, the characterization allows for identifying theintrahousehold decision structure (including the sharing rule) under the same minimalistic assumptions. Anapplication to Dutch household data demonstrates the empirical usefulness of our theoretical results.
    Keywords: marriage market; stable matching; Pareto efficient household consumption; testable implications; sharing rule identification; preference heterogeneity
    JEL: C14 D11 C78
    Date: 2014–04
  10. By: Myriam Donsimoni (PACTE - Politiques publiques, ACtion politique, TErritoires - Institut d'Études Politiques [IEP] - Grenoble - CNRS : UMR5194 - Université Pierre-Mendès-France - Grenoble II - Université Joseph Fourier - Grenoble I); Daniel Labaronne (Larefi - Laboratoire d'analyse et de recherche en économie et finance internationales - Université Montesquieu - Bordeaux IV : EA2954)
    Abstract: Nous étudions le comportement de managers d'une entreprise publique, l'Office Chérifien des Phosphates, et d'élus locaux engagés dans une relation de RSE. Quels sont les fondements théoriques de ce type de relation et les stratégies de ces acteurs ? Nous formalisons, à partir de la théorie des jeux, l'influence des managers de l'OCP sur l'action des élus. Cette influence s'exerce soit par la coopération, soit par le contrôle. Elle peut déboucher sur de l'asymétrie informationnelle générée par les élus. Nous examinons l'attitude des managers de l'OCP confrontés à cette situation biaisée pour en tirer des enseignements managériaux.
    Keywords: responsabilité sociale (M14) ; théorie des jeux (C7) ; gouvernance d'entreprise (G34) ; comportement des entreprises (D21) ; information privée et asymétrique (D 82)
    Date: 2014

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