Biologists rely extensively on the iterated Prisoner's Dilemma game to model reciprocal altruism. After examining the informal conditions necessary for reciprocal altruism, I argue that formal games besides the standard iterated Prisoner's Dilemma meet these conditions. One alternate representation, the modified Prisoner's Dilemma game, removes a standard but unnecessary condition; the other game is what I call a Cook's Dilemma. We should explore these new models of reciprocal altruism because they predict different stability characteristics for various strategies; for instance, I (...) show that strategies such as Tit-for-Tat have different stability dynamics in these alternate models. (shrink)