Open Access. Powered by Scholars. Published by Universities.®
Social and Behavioral Sciences Commons™
Open Access. Powered by Scholars. Published by Universities.®
Articles 1 - 2 of 2
Full-Text Articles in Social and Behavioral Sciences
When Non-Transitive Relations Take Maxima And Competitive Equilibria Can't Be Beat, Ted Bergstrom
When Non-Transitive Relations Take Maxima And Competitive Equilibria Can't Be Beat, Ted Bergstrom
Ted C Bergstrom
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 …
The Existence Of Maximal Elements And Equilibria In The Absence Of Transitivity, Ted Bergstrom
The Existence Of Maximal Elements And Equilibria In The Absence Of Transitivity, Ted Bergstrom
Ted C Bergstrom
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.