Our society is based on cooperation. The evolution of cooperation remains a challenging problem from the viewpoint of not only evolutionary theory but also the social sciences: the evolution of cooperation is not an easy problem to solve. We consider the prisoner’s dilemma (PD) game. Two players play the prisoner’s dilemma game and there are two types of players: cooperators and defectors. If both cooperators play the PD game, they obtain the payoff, R. If a cooperator plays the PD game with a defector, the cooperator obtains S and the defector obtains T. If both are defectors, they obtain the payoff, P. It is often assumed that the cooperator gives a benefit, b, to the opponent, incurring a cooperation cost, −c (b, c > 0), but the defector does not give anything. Therefore, T = b, R = b−c, P = 0 and S = −c. As one of the definitions satisfying the PD game is T > R > P > S, defectors obtains a greater payoff than cooperators regardless of the opponent’s type. As a result, players choose to be defectors and thus cooperation is unachievable. Therefore, previous studies on evolutionary game theory have investigated conditions whereby cooperation can evolve.