Instability in the implementation of Walrasian allocations
type: Item
instance of: scholarly article
title: Instability in the implementation of Walrasian allocations
zbMATH Open document ID: 0603.90028
DOI: 10.1016/0022-0531(86)90048-7
published in: Journal of Economic Theory
publication date: 1986-01-01T00:00:00Z
full work available at URL: http://purl.umn.edu/1798
review text: The existence of game forms which implement Walrasian allocations as Cournot (Nash) equilibrium outcomes is well known. However, if the equilibria are also required to be locally dynamically stable, at least for environments with unique Walrasian allocations, this paper shows that the requisite game forms do not exist. Our definition of a game form entails certain regularity conditions, and requires the Cournot equilibrium to be unique when the Walrasian equilibrium is unique. The main result is that for such a game form, there does not exist a continuous-time strategy adjustment process which ensures the local stability of Cournot equilibria throughout a certain class of environments having unique Walrasian equilibria. Each trader adjusts his strategy in response to his own characteristics and the observed current strategies of others; but the direction and magnitude of adjustments are not constrained by any behavioral assumptions. The definitions permit the inclusion of an artificial player, such as an auctioneer, so the well- known tatonnement instability emerges as a special case.
Mathematics Subject Classification ID: 91B50
zbMATH DE Number: 3974663
zbMATH Keywords: Walrasian allocations
zbMATH Keywords: Cournot (Nash) equilibrium outcomes
zbMATH Keywords: continuous- time strategy adjustment process
zbMATH Keywords: local stability
author: James S. Jordan
MaRDI profile type: Publication
OpenAlex ID: W2046934461
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description: scientific article; zbMATH DE number 3974663