  The Sato-Crutchfield equations are studied analytically and numerically. The
Sato-Crutchfield formulation is corresponding to losing memory. Then
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 on the previous experiences, initial conditions, and the rules of
the game itself. 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.
