ANALYSIS OF OPTIMAL SITUATION DISTRIBUTIONS IN A SPECIAL 2 x 2 BI-MATRIX GAME

We shall discuss a 2x bimatrix game which has exactly one mixed Nash equilibrium in which no strategy is pure. We shall first define the concept of optimal situation distribution that is a correlated equilibrium whose marginal distributions form the unique mixed Nash equilibrium and whose situations with positive probability are strictly pure Nash equilibria. Secondly, we shall give a method to find optimal situation distribution in the game. And finally, we shall research the optimal situation distributions in three classical games, i.e. battle of the sexes, game of chicken, and game of warriors.