One step beyond Nash Equilibrium

Abstract

The bargaining problem in two-person games is selecting a particular point (i.e., an equilibrium) in the utility set to reach a jointly optimal result. Nonetheless, there are games with no or even more than one equilibrium, where in non-zero-sum games with multiple equilibria, all equilibria do not necessarily result in the same utility set. Each player not only should play with her/his equilibrium strategies, but also (s)he would be better to select the strategy that leads her/him to a better utility than the other equilibria. We present a BNE approach consisting of three parts: a 2-layer graph representation of the game that encompasses both strategic and extensive representations; a game reduction method where all Nash Equilibria remain unchanged; and locating the best NE strategy (which results in the best social welfare among all NEs) to start with, along with determining the first mover. The study shows the computationally correctness of the approach in well-known 2×2 and different sizes of sample 2-person games.