The greater generosity of the spatialized prisoner’s dilemma

The iterated Prisoner’s Dilemma is the standard model for the evolution of cooperative behavior in a community of egoistic agents. Within that model, a strategy of “tit-for-tat” has established a reputation for being particularly robust. Nowak and Sigmund have shown that in a world of imperfect information it is not tit-for-tat that finally triumphs, however, but “generous tit-for-tat”—a variant which “forgives” with a probability of 1/3. In the present study, a spatial dimension is added to the standard model. The surprising result is that generosity is favored even more: the optimal strategy in a spatialized Prisoner’s Dilemma carries a forgiveness probability of 2/3—twice as generous as “generous tit-for-tat”.