We show that a cooperative outcome—one that is at least next-best for the players—is not a Nash equilibrium (NE) in 19 of the 57 2 x 2 strict ordinal conflict games (33%), including Prisoners’ Dilemma and Chicken. Auspiciously, in 16 of these games (84%), cooperative outcomes are nonmyopic equilibria (NMEs) when the players make farsighted calculations, based on backward induction; in the other three games, credible threats induce cooperation. More generally, in all finite normal-form games, if players’ preferences are strict, farsighted calculations stabilize at least one Pareto-optimal NME. We illustrate the choice of NMEs that are not NEs by two cases in international relations: (i) no first use of nuclear weapons, chosen by the protagonists in the 1962 Cuban missile crisis and since adopted by some nuclear powers; and (ii) the 2015 agreement between Iran, and a coalition of the United States and other countries, that has been abrogated by the United States but has forestalled Iran’s possible development of nuclear weapons.