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The Existence of Maximal Elements and Equilibria in the Absence of Transitivity

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Author Info
Ted Bergstrom (University of California, Santa Barbara)

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Abstract

This paper generalizes results of Ky Fan and Hugo Sonnenschein on the existence of maximal elements for non-transitive binary relations. It proves a generalization of Nash's theorem on the existence of non-cooperative equilibrium. It also shows that existence of competitive equilibrium can be proved as a consequence of the existence of a maximal element for an appropriately chosen binary relation.

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File URL: http://repositories.cdlib.org/cgi/viewcontent.cgi?article=1149&context=ucsbecon
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Publisher Info
Paper provided by Department of Economics, UC Santa Barbara in its series University of California at Santa Barbara, Economics Working Paper Series with number 1975C.

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Date of creation: 10 Aug 1975
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Handle: RePEc:cdl:ucsbec:1975c

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Related research
Keywords: existence of competitive equilibrium; non-transitive preferences; maximization; maximal elements ;

Cited by:
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  1. Ted Bergstrom, 2003. "When Non-transitive Relations Take Maxima and Competitive Equilibria Can't Be Beat," University of California at Santa Barbara, Economics Working Paper Series 1992A, Department of Economics, UC Santa Barbara. [Downloadable!]
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  2. Norman Schofield & Robert P. Parks, 1993. "EXISTENCE OF NASH EQUILIBRIUM IN A SPATIAL MODEL OF n-PARTY COMPETITION," Public Economics 9308002, EconWPA, revised 25 Aug 1993. [Downloadable!]
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This page was last updated on 2009-12-12.

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