  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.
