Sato-crutchfield formulation for some evolutionary games

The Sato-Crutchfield equations are analytically and numerically studied. The Sato-Crutchfield formulation corresponds to losing memory. Then the Sato-Crutchfield formulation is applied for some different types of games including hawk-dove, prisoner's dilemma and the battle of the sexes games. The Sato-Crutchfield formulation is found not to affect the evolutionarily stable strategy of the ordinary games. But choosing a strategy becomes purely random, independent of the previous experiences, initial conditions, and the rules of the game itself. The Sato-Crutchfield formulation for the prisoner's dilemma game can be considered as a theoretical explanation for the existence of cooperation in a population of defectors.