Non-zero-sum two-person games

This chapter is devoted to the study of Nash equilibria, and correlated equilibria in both finite and infinite games. We restrict our discussions to only those properties that are somewhat special to the case of two-person games. Many of these properties fail to extend even to three-person games. The existence of quasi-strict equilibria, and the uniqueness of Nash equilibrium in completely mixed games, are very special to two-person games. The Lemke-Howson algorithm and Rosenmuller's algorithm which locate a Nash equilibrium in finite arithmetic steps are not extendable to general n-person games. The enumerability of extreme Nash equilibrium points and their inclusion among extreme correlated equilibrium points fail to extend beyond bimatrix games. Fictitious play, which works in zero-sum two-person matrix games, fails to extend even to the case of bimatrix games. Other algorithms that would locate certain refinements of Nash equilibria are also discussed. The chapter also deals with the structure of Nash and correlated equilibria in infinite games.