This paper studies the possibility of whole population cooperation based on differentabilities of players. Consider the following infinitely repeated game, similar to Ghosh andRay (1996). At each stage, uncountable numbers of players, who are randomly matchedwithout information about their partners’ past actions, play a prisoner’s dilemma game. Theplayers have the option to continue their relationship, and they all have the same discountfactor. Also, they have two possible types: high ability player (H) or low ability player (L). Hcan produce better outcomes for his partner as well as for himself than L can. We look for anequilibrium that is robust against both pair-wise deviation and individual deviation, andcall such equilibrium a social equilibrium. In this setting, long-term cooperative behavioramong 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.