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When Non-transitive Relations Take Maxima and Competitive Equilibria Can't Be Beat

Ted Bergstrom, University of California, Santa Barbara

Abstract

The paper generalizes theorems of Ky Fan and Hugo Sonnenschein on the existence of maximal elements for non-transitive relations. I used these results to show that a binary relation could be constructed whose maximal element must be a competitive equilibrium. Thus proving the existence of competitive equilibrium under somewhat more general conditions than had been done previously. In 1975, I thought this was a useful extension of the Gale Mas Collel existence theorem. Journal referees then didn't agree with me, so I let it ripen in my desk for 15 years. I still think it is worth looking at if you are interested in the existence of competitive equilibrium or in maximization of funny preference orderings.

Suggested Citation

Ted Bergstrom. "When Non-transitive Relations Take Maxima and Competitive Equilibria Can't Be Beat" Economic Theory and International Trade. Ed. William Neuefeind. Verlin: Springer Verlag, 2003. 29-52.