Weak Berge Equilibrium

Abstract

Various concepts of solutions can be employed in the non-cooperative game theory. The Berge equilibrium is one of such solutions. The Berge equilibrium is an altruistic concept of equilibrium. In this concept, the players act on the principle “One for all and all for one!” The Berge equilibrium solves such well known paradoxes in the game theory as the “Prisoner’s Dilemma”, “Battle of the sexes” and many others. At the same time, the Berge equilibrium rarely exist 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 properties of the weak Berge equilibrium have been investigated. The existence of the weak Berge equilibrium in mixed strategies has been established for finite games. A numerical weak Berge equilibrium approximate search method, based on 3LP-algorithm, is proposed. The weak Berge equilibria for finite 3-person non-cooperative games are computed.