Condicions suficients per equilibri de Nash i models de diferenciació espacial

Abstract

[en] The Cournot competition model created in 1838 is the predecesor of the application of game theory to find equilibrium conditions for the competition. This work starts with the concepts of game theory developed during the twentieth century to be able to study spatial competition models of Hotelling’s type and several dimensions. An equilibrium existence theorem for n-dimensional models with any m firms will be presented. This theorem was proposed by Caplin and Nalebuff in 1991 and we will detail the formal proof to show the relation between the assumptions made in the model and the final result. These results will be used to find an equilibrium in a specific model of spatial competition in two dimensions.