Computation the Weak Berge Equilibrium in Finite 3-Person Games

Abstract

Various concepts of solutions can be employed in non-cooperative game theory. A Berge equilibrium is one such solutions. The Berge equilibrium is altruistic concept of equilibrium. In this concept, the players act on the principle of “One for all and all for one!” The Berge equilibrium solves such well known paradoxes in game theory as the “Prisoner’s Dilemma”, “Battle of the sexes” and many others. At the same time, Berge equilibrium rarely exists in pure strategies. Moreover, in finite games, the Berge equilibrium may not exist in the class of mixed strategies. The paper proposes the concept of a weak Berge equilibrium. Unlike the Berge equilibrium, the moral basis of this equilibrium is the Hippocratic Oath “First do no harm”. On the other hand, all Berge equilibria are some weak Berge equilibria. The existence of weak Berge equilibrium in mixed strategies has been established for finite games. A numerical weak Berge equilibrium approximate search method, based on 3LP-algorithm, was proposed. The weak Berge equilibrium for finite three-person non-cooperative games were computed.