analysis of a nonlinear operator in the frame of evolutionary game for dual random markets

We study the evolutionary dynamic of population, com- posed of two kinds of individuals, distributed randomly. in this game, evolution takes place in dierent periods of time between individuals fre- quently. we present a continuous nonlinear operator, which describes and fullls this discrete time evolutionary game. furthermore, we set up the adequate mathematical framework to obtain the xed point of this operator. based on this equilibrium state of the evolutionary operator, it is proved the possessions of the individuals vanish.