An Alternative Interpretation of Mixed Strategies in n-Person Normal Form Games via Resource Allocation

Abstract

In this paper , we give an interpretation of mixed strategies in normal form games via resource allocation games, where all players utilize the same resource. We define a game in normal form such that each player allocates to each of his pure strategies a fraction of the maximum resource he has available. However, he does not necessarily allocate all of the resource at his disposal. The payoff functions in the resource allocation games vary with how each player allocates his resource. We prove that a Nash equilibrium always exists in mixed strategies for n - person resource allocation games. On the other hand, we show that a mixed Berge equilibrium may not exist in such games.