Novel Dominance Principle based Approach to the Solution of Two Persons General Sum Games with n by m Moves

In a previous paper [1] the application of the dominance principle was proposed to find the non-cooperative solution of the two by two general sum game with mixed strategies; in this way it was possible to choose the equilibrium point among the classical solutions avoiding the ambiguity due to their non-interchangeability, moreover the non-cooperative equilibrium point was determined by a new geometric approach based on the dominance principle. Starting from that result it is here below proposed the extension of the method to two persons general sum games with n by m moves. The algebraic two multi-linear forms of the expected payoffs of the two players are studied. From these expressions of the expected payoffs the derivatives are obtained and they are used to express the probabilities distribution on the moves after the two definitions as Nash and prudential strategies [1]. The application of the dominance principle allows to choose the equilibrium point between the two solutions avoiding the ambiguity due to their non-interchangeability and a conjecture about the uniqueness of the solution is proposed in order to solve the problem of the existence and uniqueness of the non-cooperative solution of a two persons n by m game. The uniqueness of the non-cooperative solution could be used as a starting point to find out the cooperative solution of the game too. Some games from the sound literature are discussed in order to show the effectiveness of the presented procedure.