Some New Results for Equilibria of N-Person Games

Abstract

In this dissertation, we present four journal articles in the area of game theory. In the first article, we define a generalized equilibrium for n−person normal form games. We prove that the Nash equilibrium and the mixed Berge equilibrium are special cases of the generalized equilibrium. In the second article, we study the computational complexity of finding a mixed Berge equilibrium in n−person normal form games. In particular, we prove that the problem is an NP-complete problem for n >= 3. In the third article, we give an interpretation of mixed strategies via resource allocation. Finally, in the fourth article, we extend the concept of the mixed Berge equilibrium to n−person extensive form games.