Instability in the implementation of Walrasian allocations

J. S. Jordan

Research output: Contribution to journalArticle

16 Scopus citations

Abstract

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.

Original languageEnglish (US)
Pages (from-to)301-328
Number of pages28
JournalJournal of Economic Theory
Volume39
Issue number2
DOIs
StatePublished - Aug 1986

All Science Journal Classification (ASJC) codes

  • Economics and Econometrics

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