Decentralized Pricing and the equivalence between Nash and Walrasian equilibrium

We introduce, in the standard exchange economy model, market games in which agents use private prices as strategies. We give conditions on the game form that ensure that the only strict Nash equilibria of the game are the competitive equilibria of the underlying economy. This equivalence result has two main corollaries. First, it adds to the evidence that competitive equilibria can be strategically stable even in small economies. Second, it implies that competitive equilibria have good local stability properties under a large class of evolutionary learning dynamics.

[1]  F. Vega-Redondo.  The evolution of Walrasian behavior , 1997 .

[2]  J. Potier,et al.  Léon Walras et le statut de la concurrence: une étude à partir des Elements d'économie politique pure , 2005 .

[3]  Douglas Gale,et al.  Bargaining and Competition Part I: Characterization , 1986 .

[4]  E. Hopkins.  Two Competing Models of How People Learn in Games (first version) , 1999 .

[5]  P. Newman,et al.  The Theory Of General Economic Equilibrium , 1964 .

[6]  Herbert Gintis,et al.  The Dynamics of General Equilibrium , 2007 .

[7]  Sayantan Ghosal,et al.  Retrading in market games , 2004, J. Econ. Theory.

[8]  Carlos Alós-Ferrer,et al.  An Evolutionary Model of Bertrand Oligopoly , 2000, Games Econ. Behav..

[9]  H. Scarf.  Some Examples of Global Instability of the Competitive Equilibrium , 1960 .

[10]  Karl Shell,et al.  Liquid markets and competition , 1990 .

[11]  D. Fudenberg,et al.  The Theory of Learning in Games , 1998 .

[12]  D. Friedman.  A simple testable model of double auction markets , 1991 .

[13]  Variations on the Theme of Scarf's Counter-Example , 2004 .

[14]  M. Benaïm,et al.  Deterministic Approximation of Stochastic Evolution in Games , 2003 .

[15]  Antoine Mandel,et al.  Stochastic stability in the Scarf economy , 2014, Math. Soc. Sci..

[16]  Charles R. Plott,et al.  Global instability in experimental general equilibrium: the Scarf example , 2004, J. Econ. Theory.

[17]  O. Volij,et al.  Mistakes in Cooperation: The Stochastic Stability of Edgeworth's Recontracting , 2003 .

[18]  Herbert Gintis,et al.  Game Theory Evolving: A Problem-Centered Introduction to Modeling Strategic Interaction - Second Edition , 2009 .

[19]  C. Cannings,et al.  Evolutionary Game Theory , 2010 .

[20]  K. Schlag.  Why Imitate, and If So, How?, : A Boundedly Rational Approach to Multi-armed Bandits , 1998 .

[21]  P. Hammond.  IRREDUCIBILITY, RESOURCE RELATEDNESS, AND SURVIVAL IN EQUILIBRIUM WITH INDIVIDUAL NONCONVEXITIES , 1993 .

[22]  Andrew McLennan,et al.  SEQUENTIAL BARGAINING AS A NONCOOPERATIVE FOUNDATION FOR WALRASIAN EQUILIBRIUM , 1991 .

[23]  Jörgen W. Weibull,et al.  Evolutionary Game Theory , 1996 .

[24]  G. Giraud.  Strategic market games: an introduction , 2003 .

[25]  Alexander Matros,et al.  Competitive behavior in market games: Evidence and theory , 2011, J. Econ. Theory.

[26]  C. Shalizi.  Dynamics of Bayesian Updating with Dependent Data and Misspecified Models , 2009, 0901.1342.

[27]  Monique Florenzano,et al.  General Equilibrium Analysis: Existence and Optimality Properties of Equilibria , 2003 .

[28]  Fernando Vega Redondo,et al.  The evolution of walrasian behavior , 1996 .

[29]  John Dickhaut,et al.  Price Formation in Double Auctions , 2001, E-Commerce Agents.

[30]  Y. Balasko.  The Equilibrium Manifold: Postmodern Developments in the Theory of General Economic Equilibrium , 2009 .

[31]  L. Walras.  Elements of Pure Economics , 1954 .

[32]  V. Smith.  Microeconomic Systems as an Experimental Science , 1982 .

[33]  H. Young,et al.  The Evolution of Conventions , 1993 .

[34]  Jean-Michel Grandmont,et al.  Temporary General Equilibrium Theory , 1977 .

[35]  H. Gintis,et al.  Price dynamics, financial fragility and aggregate volatility , 2015 .

[36]  Takashi Kunimoto,et al.  Bargaining and Competition Revisited , 2002, J. Econ. Theory.

[37]  L. Shapley,et al.  Trade Using One Commodity as a Means of Payment , 1977, Journal of Political Economy.

[38]  Evolution of Walrasian equilibrium in an exchange economy , 2011 .

[39]  E. Kalai,et al.  OTHER SOLUTIONS TO NASH'S BARGAINING PROBLEM , 1975 .

[40]  A. Rubinstein.  Perfect Equilibrium in a Bargaining Model , 1982 .

[41]  A. Ianni,et al.  Learning strict Nash equilibria through reinforcement , 2011 .

[42]  J. Ledyard,et al.  Theories of price formation and exchange in double oral auctions , 1986 .

[43]  Herbert Gintis,et al.  Markov models of social dynamics: Theory and applications , 2013, TIST.

[44]  Douglas Gale,et al.  Bargaining and Competition Part II: Existence , 1986 .

[45]  A. Rubinstein,et al.  Equilibrium in a market with sequential bargaining , 1985 .