This paper studies the possibility of whole population cooperation based on different abilities of players. Consider the following infinitely repeated game, similar to Ghosh and Ray (1996). At each stage, uncountable numbers of players, who are randomly matched without information about their partners` past actions, play a prisoner`s dilemma game. The players have the option to continue their relationship, and they all have the same discount factor. Also, they have two possible types: high ability player (H) or low ability player (L). H can produce better outcomes for his partner as well as for himself than L can. We look for an equilibrium that is robust against both pair-wise deviation and individual deviation, and call such equilibrium a social equilibrium. In this setting, long-term cooperative behavior among the whole population can take place in a social equilibrium because of the players` preference for their partners` ability. In addition, a folk theorem of this model is proposed.