The 2 x 2 games, most notably the Prisoner's Dilemma, have been extensively used in studies into reciprocal cooperation and, to a lesser extent, kin selection. This paper considers the suitability of the 2 x 2 games in this role as an interaction model for studying the evolution of cooperation through reciprocation and kin selection. This consideration is not restricted to the Prisoner's Dilemma, but includes the other non-trivial symmetric 2 x 2 games. In particular the different games are assessed with regard to whether they provide support for reciprocal cooperation, kin selection for altruism, or both. It is concluded that the popularity of the Prisoner's Dilemma as a means of representing social and biotic interaction is justified by its superiority according to these criteria. This conclusion is tempered, however, by the identification of several limitations in the simplest conditional form of the Prisoner's Dilemma, that with deterministic one-dimensional strategies. The most important of these are: that kin selection for "strong altruism" can only occur under certain circumstances, that kin selection for altruism is self-interfering under certain circumstances, and that kin selection for altruism may undermine selection for effective reciprocating strategies under certain circumstances. These limitations provide a benchmark against which to measure applications of the 2 x 2 games in modelling reciprocal cooperation and kin selection, both in isolation and in the interesting case in which they operate simultaneously, and suggest the requirement for a new interaction model for future investigations.