In this paper a class of large supergames, i.e., infinitely repeated games played by many players are studied. The players located on the vertex set of planar rectangle lattice play several basic games with his neighbors. The basic game is two-person prisoners’ dilemma game with asymmetric payoffs. Under the conditions of the pre-specified updating rules and the transition probabilities, the relevant stochastic process of strategy evolution forms a Markovian process. The simulation results about the long-run behavior are provided.