This paper develops a model of rational behavior that is found to be compatible with the evolution of China-U.S. relations from the early 1970s to the late 1980s. The authors introduce countervailing strategies that broaden our understanding of what is rational in a game-theoretic context. Countervailing behavior accommodates inertia and delay, as well as reactivity, and is shown to be involved in every equilibrium strategy. The terms of the interaction between the United States and China are identified in light of a countervailing model, and the payoff structure that supports the observed dynamic interaction is inferred. Prior to 1979, which marks the inception of Chinas open-door policy, the payoff structure found conforms to a little-known mixed-motive game, whereas the 1980s are characterized by a Prisoner's Dilemma. In the 1980s rational play involves positive reactivity on the part of each country, while prior to 1979 rational behavior on the part of the U.S. takes the form of an inverse response to Chinese initiatives, a behavior that draws its rationality from its ability to move China to a more cooperative stance despite a Deadlock-type payoff structure.