The Stability of Walrasian General Equilibrium with Decentralized Price Adjustment Herbert Gintis and Antoine Mandel∗† September 30, 2014 Abstract We study a completely decentralized Walrasian general equilibrium econ- omy with trade occurring out of equilibrium. Prices are fully controlled by economic agents and updated according to an evolutionary learning process. This approach to price dynamics overcomes the failure of a centralized price adjustment process (tˆatonnement) to provide dynamical foundations for gen- eral equilibrium. In our setting, the law of one-price, price-taking behavior and market equilibrium are stochastically approximated long-run emergent properties of a complex dynamical system. Journal of Economic Literature Classifications: C62—Existence and Stability Conditions of Equilibrium D51—Exchange and Production Economies D58—Computable and Other Applied General Equilibrium Economies 1 Introduction Walras (1874) developed a general model of competitive market exchange, but provided only an informal argument for the existence of a market-clearing equi- librium for this model. Wald (1951[1936]) provided a proof of existence for a simplified version of Walras’ model. This proof was substantially generalized by Debreu (1952), Arrow and Debreu (1954), Gale (1955), Nikaido (1956), McKenzie (1959), Negishi (1960), and others. ∗The authors contributed equally to this research. Gintis: Santa Fe Institute; Mandel: Paris School of Economics, University of Paris 1 Panth´eon-Sorbonne. The authors acknowledgethe support of In- stitute for New Economic Thinking grant INO1200022. Antoine Mandel also acknowledgessupport from the EU-FP7 project SIMPOL. We dedicate this paper to Hirofumi Uzawa. He will be sorely missed. †Corresponding author, email:
[email protected], tel/fax:+3314407 8271/8301 1 The stability of the Walrasian economy became a central research focus in the years following the existence proofs (Arrow and Hurwicz 1958, 1959, 1960; Ar- row, Block and Hurwicz 1959; Nikaido 1959; McKenzie 1960; Nikaido and Uzawa 1960).