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.