Game theory paradigms like the Prisoner’s Dilemma have provided an extremely successful avenue for mathematical and computational analysis of emergent dynamics in a wide array of social science situations. However, simple 2x2 games fail to capture more complex interactions involving multiple parties and changing payoffs. In this paper, we propose an elaboration of the Iterated Prisoner’s Dilemma paradigm to capture the dynamics of power between groups of competing and cooperating individuals. The new game, IPD^2, features two levels of competition and cooperation both within and between groups of individuals. We present results of simulations involving several simple agents that allow us to explore the dynamics of the game. Finally, we discuss the various social science phenomena that this game will allow us to study systematically through both the collection of human data and simulation of automated agents.