Author(s)： Shin-ichiro Takazawa

J. Math-for-Ind. 2B (2010) 227-234.

• File： JMI2010B-11.pdf (121KB)

Abstract
The behavior to decide the action according to the current situation is seen well in humans. We consider the prisoner's dilemma in which the variable probability of cooperation is allowed. Here, we define a wait-and-see strategy as the strategy that an individual cooperates at the same probability as the proportion of cooperation in the population. In addition, we consider a game between relatives in which an individual is more likely to meet an opponent using the same strategy. To examine the reasonableness of a wait-and-see strategy from the viewpoint of survival, we analyze the three strategies in the prisoner's dilemma between relatives by means of a replicator dynamics. We prove that our wait-and-see strategy survives in almost all conditions for the prisoner's dilemma between relatives. Therefore, we conclude a wait-and-see behavior is reasonable.

Keyword(s).　 wait-and-see strategy, prisoner's dilemma, game between relatives, survival, replicator dynamics