Noncooperative N-person game theory (N≥2) using expected relative desirability criterion

Abstract

Considered is noncooperative discrete N-person game theory forN≥2 (where the players choose their strategies separately and independently). Payoffs can be of a very general nature and are not necessarily numbers. However, each player is able to quantitatively specify the relative desirability of the possible game outcomes (N-dimensional, a pay off to each player) according to his preferences. That is, he specifies a positive number for each outcome and these numbers are such that their ratios quantitatively represent the relatively desirability of the corresponding outcomes to this player. For each player, the criterion is the expected relative desirability to him of what occurs for the game, and an optimum mixed strategy maximizes the minimum value of this criterion over all possible mixed strategies that could be used by the other players. An optimum solution is obtained by used of classical minimax game theory. Practical implications of applying thisN-person game theory are examined. Also, a possible approach for developing quantitative functions to provide the relative desirability numbers is outlined.