Theorists of cooperation argue that reciprocity combined with cooperative initiatives can allow cooperation to emerge between self-interested actors caught in collective goods dilemmas and lacking binding authority. Cooperation among the world's great powers is a key testing ground for such theories. Using U.S.-Chinese relations as a focus, this article develops a formal, decision-theoretic, model of great-power relations. The model is based on the empirical evidence from the Three-Way Street study of the U.S.-Soviet-Chinese triangle during the Cold War. The empirical results are used to construct stylized conditions that restrict the model in ways corresponding to our best empirical knowledge of great-power relations. These restrictions allow the model to be simplified (becoming decision-theoretic rather than game-theoretic), without losing empirical realism. The restrictions also allow the model to be generalized in several ways; it allows for graduated play along a scale of cooperation-conflict and for limited (partial) reciprocity in response to movements along that scale. Payoffs are defined along a scale of severity (relative incentives to defect vs. cooperate) in games of Prisoner's Dilemma, Stag Hunt, Chicken, Deadlock, or Harmony. The model implies that limited reciprocity is surprisingly effective in creating the conditions for cooperation to emerge, under a range of payoff structures and realistic discounting of future outcomes.
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