1202.0187 (Jelena Grujić et al.)

On the coexistence of cooperators, defectors and conditional cooperators
in the multiplayer iterated Prisoner's Dilemma    [PDF]

Jelena Grujić, José A. Cuesta, Angel Sánchez

Recent experimental evidence [Gruji\'c et al., PLoS ONE 5, e13749 (2010)] on
the spatial Prisoner's Dilemma suggests that players choosing to cooperate or
not on the basis of their previous action and the actions of their neighbors
coexist with steady defectors and cooperators. We here study the coexistence of
these three strategies in the multiplayer iterated Prisoner's Dilemma by means
of the replicator dynamics. We consider groups with n = 2, 3, 4 and 5 players
and compute the payoffs to every type of player as the limit of a Markov chain
where the transition probabilities between actions are found from the
corresponding strategies. We show that for group sizes up to n = 4 there exists
an interior point in which the three strategies coexist, the corresponding
basin of attraction decreasing with increasing number of players, whereas we
have not been able to locate such a point for n = 5. We analytically show that
in the infinite n limit no interior points can arise. We conclude by discussing
the implications of this theoretical approach on the behavior observed in
experiments.

View original: http://arxiv.org/abs/1202.0187