The Dynamics of General Equilibrium

In Walras original description of general equilibrium (Walras, 1954 [1874]), market clearing was effected by a central authority. This authority, which has come to be known as the auctioneer, remains today because no one has succeeded in producing a plausible decentralised dynamic model of producers and consumers engaged in market interaction in which prices and quantities move towards market-clearing levels. Only under implausible assumptions can the continuous auctioneer dynamic be shown to be stable (Fisher, 1983), and in a discrete model, even these assumptions (gross substitutability, for instance) do not preclude instability and chaos in price movements (Saari, 1985; Bala and Majumdar, 1992). 1 Moreover, contemporary analysis of excess demand functions suggests that restrictions on preferences are unlikely to entail the stability of t^ (Sonnenschein, 1972, 1973; Debreu, 1974; Kirman and Koch, 1986). It has been a half century since Debreu (1952) and Arrow and Debreu (1954) provided a satisfactory analysis of the equilibrium properties market economies, yet we know virtually nothing systematic about Walrasian dynamics. This suggests that we lack understanding of one or more fundamental properties of market exchange. This article provides an agent-based model of the Walrasian economy. An agentbased model is a computer simulation of the repeated play of a game in which a large number of agents are endowed with software-encoded strategies governing both how they play the game and how they gather information and update their behaviour. The disequilibrium behaviour of agents in our agent-based models is governed by a replicator dynamic (Taylor and Jonker, 1978) in which, over time, successful agents tend in Darwinian fashion to increase in frequency at the expense of unsuccessful agents. We describe the process of shifting from lower to higher payoff strategies as imitation,

[1]  M. Hirota.  On the Probability of the Competitive Equilibrium Being Globally Stable: The C.E.S. Example , 2002 .

[2]  M. Freidlin,et al.  Random Perturbations of Dynamical Systems , 1984 .

[3]  D. Gale.  A NOTE ON GLOBAL INSTABILITY OF COMPETITIVE EQUILIBRIUM , 1963 .

[4]  Duncan K. Foley,et al.  A Statistical Equilibrium Theory of Markets , 1994 .

[5]  On the Stability of Competitive Equilibrium and the Patterns of Initial Holdings: An Example , 1981 .

[6]  D. E. Goldberg,et al.  Genetic Algorithms in Search , 1989 .

[7]  W. R. Buckland,et al.  Proceedings of the Second Berkeley Symposium on Mathematical Statistics and Probability. , 1952 .

[8]  Hugo Sonnenschein,et al.  Market Excess Demand Functions , 1972 .

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

[10]  Claus Weddepohl.  Simulating tatonnement in a production economy , 1997 .

[11]  S. Smale.  Dynamics in General Equilibrium Theory , 1976 .

[12]  Frank Hahn,et al.  General equilibrium : problems and prospects , 2003 .

[13]  J. Stevenson.  The cultural origins of human cognition , 2001 .

[14]  William Feller,et al.  An Introduction to Probability Theory and Its Applications , 1967 .

[15]  G. Debreu,et al.  Excess demand functions , 1974 .

[16]  Herbert Gintis,et al.  The Revenge of Homo Economicus: Contested Exchange and the Revival of Political Economy , 1993 .

[17]  K. Arrow,et al.  EXISTENCE OF AN EQUILIBRIUM FOR A COMPETITIVE ECONOMY , 1954 .

[18]  William M. Fields,et al.  The Cultural Origins of Human Cognition. , 2000 .

[19]  F. Fisher.  Disequilibrium Foundations of Equilibrium Economics , 1984 .

[20]  Gérard Debreu.  Economies with a Finite Set of Equilibria , 1970 .

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

[22]  S. Thompson.  Social Learning Theory , 2008 .

[23]  A. Smithies.  The Stability of Competitive Equilibrium , 1942 .

[24]  Goldberg,et al.  Genetic algorithms , 1993, Robust Control Systems with Genetic Algorithms.

[25]  Donald G. Saari,et al.  Iterative Price Mechanisms , 1985 .

[26]  Harald Uhlig,et al.  Solving Nonlinear Stochastic Growth Models: a Comparison of Alternative Solution Methods , 1989 .

[27]  Sun Xiaomeng,et al.  Agent-based Microsimulation of Economy from A Complexity Perspective , 2000 .

[28]  L. Dworsky.  An Introduction to Probability , 2008 .

[29]  P. Taylor,et al.  Evolutionarily Stable Strategies and Game Dynamics , 1978 .

[30]  A. Kirman,et al.  Market Excess Demand in Exchange Economies with Identical Preferences and Collinear Endowments , 1986 .

[31]  L. Hurwicz,et al.  ON THE STABILITY OF THE COMPETITIVE EQUILIBRIUM, I1 , 1958 .

[32]  Venkatesh Bala,et al.  Chaotic tatonnement , 1993 .

[33]  Peter S. Albin,et al.  Decentralized, dispersed exchange without an auctioneer: A simulation study , 1992 .

[34]  A. Mas-Colell,et al.  Microeconomic Theory , 1995 .

[35]  Benedikt Stefansson.  Swarm: An Object Oriented Simulation Platform Applied to Markets and Organizations , 1997, Evolutionary Programming.

[36]  L. McKenzie.  STABILITY OF EQUILIBRIUM AND THE VALUE OF POSITIVE EXCESS DEMAND , 1960 .

[37]  P. A. P. Moran,et al.  An introduction to probability theory , 1968 .

[38]  P. Kattuman,et al.  One Market, One Money, One Price? Price Dispersion in the European Union , 2004 .

[39]  David E. Goldberg,et al.  Genetic Algorithms in Search Optimization and Machine Learning , 1988 .

[40]  Nancy Argüelles,et al.  Author ' s , 2008 .

[41]  P. Garegnani,et al.  Heterogeneous Capital, the Production Function and the Theory of Distribution , 1970 .

[42]  Gerard Debreu,et al.  A Social Equilibrium Existence Theorem* , 1952, Proceedings of the National Academy of Sciences.

[43]  K. Arrow.  An Extension of the Basic Theorems of Classical Welfare Economics , 1951 .

[44]  H. Gintis.  Some implications of endogenous contract enforcement for general equilibrium theory , 2003 .

[45]  H. Sonnenschein.  Do Walras' identity and continuity characterize the class of community excess demand functions? , 1973 .

[46]  John H. Holland,et al.  Adaptation in Natural and Artificial Systems: An Introductory Analysis with Applications to Biology, Control, and Artificial Intelligence , 1992 .

[47]  Charles R. Plott,et al.  General equilibrium, markets, macroeconomics and money in a laboratory experimental environment , 1998 .

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

[49]  M. Hirota.  Global stability in a class of markets with three commodities and three consumers , 1985 .