Berge equilibrium in normal form static games: a literature review

Example of a Finite Game with No Berge Equilibria at All

“…The problem whether we should expect the same in games with a bigger number of players was posed as the Open Problem No. 1 in [5]. Our counterexample shows that already among three-person games there exist games with no Berge equilibria at all.…”

“…Therefore, we adopt the following definition that extends to mixed strategies the original definition [6]. Figure 1: Best support correspondences bs i (·) corresponding to game (5).…”

“…Sometimes it is claimed (cf. [5]) that in such cases the concept of Berge equilibrium could be of some help. So, let us study Berge equilibria in this game.…”

“…Brief description of historical development of the idea of Berge equilibrium can be found in a paper[2]. See also very extensive review of literature on Berge equilibria[5].…”

Weak Berge Equilibrium in Finite Three-person Games: Conception and Computation

“…Another interpretation of the Berge equilibrium is [8] the Golden Rule of morality: "Treat others the way you want to be treated". The development of the Berge equilibrium concept is described in details in the review [9]. It is worth noting that the Berge equilibrium solves such well known paradoxes in game theory as the "Prisoner's Dilemma", "Battle of the sexes" and many others.…”