Diverse Behavior Patterns in a Symmetric Society with Voluntary Partnerships

In the literature of voluntarily repeated Prisoner's Dilemma, the focus is on how long-term cooperation is established, when newly matched partners cannot know the past actions of each other. In this paper we investigate how non-cooperative and cooperative players co-exist. In many incomplete information versions of a similar model, inherently non-cooperative players are assumed to exist in the society, but their long-run fitness has not been analyzed. In reality and in experiments, we also observe that some people are cooperative, while others never cooperate. We show that a bimorphic equilibrium of the most cooperative strategy and the most myopic strategy exists for sufficiently high survival rate of players, and that it is evolutionarily stable under uncoordinated mutations. For lower survival rates, adding initial periods of defection makes similar bimorphic equilibria. Both types of equilibria confirm persistence of defectors.