A new tensor approach of computing pure and mixed Unilateral Support Equilibria

Abstract

In this paper, pure unilateral support equilibrium (USE) is located among pure Nash and pure Berge equilibrium using tensors. The differences between these equilibria are shown using tensor form of a game and are illustrated with numerical examples. Tensors will help specify the location of each equilibrium using a system of coordinates that brings a solid mathematical foundation of all equilibria and provides the possibility to solve high dimensional problems. A numerical example with a 15-player game is studied to demonstrate the efficiency. Besides, we extend the notion of pure USE to mixed USE when the sets of strategies of all players are finite. We prove a lemma dedicated to inaugurate a method of computing mixed USE profiles. We write corresponding formulas using tensors and their operations, and then we illustrate the new method and lemma method by a numerical example of a 7-player game.