Universally converging adjustment processes - a unifying approach

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Abstract

Both in game theory and in general equilibrium theory, there exists a number of universally converging adjustment processes. In game theory, these processes typically serve the role of selecting a Nash equilibrium. Examples are, the tracing procedure of Harsanyi and Selten or the equilibrium selection procedure proposed by McKelvey and Palfrey. In general equilibrium, the processes are adjustment rules by which an auctioneer can clear all markets. Examples are the processes studied by Smale, Kamiya, van der Laan and Talman, and Herings. The underlying reasons for convergence have remained rather mysterious in the literature, and convergence of different processes has seemed unrelated. This paper shows that convergence of all these processes relies on Browder's fixed point theorem. (C) 2002 Elsevier Science B.V. All rights reserved.

Original languageEnglish
Pages (from-to)341-370
Number of pages30
JournalJournal of Mathematical Economics
Volume38
Issue number3
Publication statusPublished - Nov 2002
Externally publishedYes

Keywords

  • adjustment processes
  • game theory
  • general equilibrium
  • universal convergence
  • EXCESS DEMAND FUNCTIONS
  • EQUILIBRIUM
  • GAMES
  • HOMOTOPY

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