The Dynamics of General Equilibrium

Abstract

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,