On the suitability of the 2 x 2 games for studying reciprocal cooperation and kin selection

Abstract

The 2 x 2 games, in particular the Prisoner's Dilemma, have been extensively used in studies into reciprocal cooperation and, to a lesser extent, kin selection. This paper examines the suitability of the 2 x 2 games for modelling the evolution of cooperation through reciprocation and kin selection. This examination is not restricted to the Prisoner's Dilemma, but includes the other non-trivial symmetric 2 x 2 games. We show that the popularity of the Prisoner's Dilemma for modelling social and biotic interaction is justified by its superiority according to these criteria. Indeed, the Prisoner's Dilemma is unique in providing the simplest support for reciprocal cooperation, and additive kin-selected altruism. However, care is still required in choosing the particular Prisoner's Dilemma payoff matrix to use. This paper reviews the impact of non-linear payoffs for the application of Hamilton's rule to typical altruistic interactions, and derives new results for cases in which the roles of potential altruist and beneficiary are separated. In doing so we find the same equilibrium condition holds in continuous games between relatives, and in discrete games with roles.