Global convergence of the stochastic tatonnement process

Ermoliev, Y.M., Keyzer, M.A., & Norkin, V.I. (2000). Global convergence of the stochastic tatonnement process. Journal of Mathematical Economics 34 (2) 173-190. 10.1016/S0304-4068(00)00037-9.

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The paper introduces stochastic elements into the Walrasian tâtonnement process, both to make it more realistic and to ensure its global convergence, with probability 1. It is assumed that the aggregate excess demand satisfies standard assumptions but is subject to measurement error. We distinguish two cases. First, the true aggregate excess demand is assumed to satisfy the Weak Axiom of Revealed Preference. This condition will be met if the underlying economy has a single consumer, several consumers with identical homothetic utility functions, or if it maximizes a social welfare function. We prove that after two minor modifications, under a fairly general specification of the measurement error and by imposing a certain consistency property on the estimator of excess demand, the tâtonnement process converges with probability 1 to an equilibrium. Second, we consider the case that the Weak Axiom only holds around some of the equilibria. The procedure proposed imposes a random shock at time intervals of increasing duration. We also discuss how the procedure could be extended to determine all equilibria, to deal with jumps in excess demand including those that do not satisfy the Weak Axiom, and to represent agents who only gradually learn how to find an optimum.

Item Type: Article
Uncontrolled Keywords: Stochastic tâtonnement; Path dependence; Stochastic optimization; Martingales; Simulated annealing
Research Programs: Risk, Modeling and Society (RMS)
Depositing User: IIASA Import
Date Deposited: 15 Jan 2016 02:11
Last Modified: 27 Aug 2021 17:16

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