EQUIVALENT REPRESENTATIONS OF BI-MATRIX GAMES

A bi-matrix game is said to be rational if the two players' common knowledge contains and only contains these: (1) The two players. (2) For either player, a set of actions. (3) Payoffs received by either player for the pair of the actions. (4) Either of players knowing the principle of maximum entropy. In this paper, we put forward a concept of Neumann-Morgenstern stable set (briefly, N-M stable set) which is a subset of set of all pure Nash equilibria in a bi-matrix game. Give an algorithm of finiding N-M statble set. Prove existence and uniqueness of N-M stable set in a bi-matrix game with at least one pure Nash equilibrium. An ideal game is defined as the game whose two p layers have the same preferences for all pure situations in the N-M stable. For example, a rational game is an ideal game. We prove that every bi-matrix game is equivalent to one and only one ideal game.