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Assume in a 2-person game that one player, Predictor (P), does not have a dominant strategy but can predict with probability p > 1/2 the strategy choice of an opponent, Predictee (Q). Q chooses a strategy that maximizes her expected payoff, given that she knows p—but not P’s prediction—and that P will act according to his prediction. In all 2 2 strict ordinal games in which there is a unique Pareto-inferior Nash equilibrium (Class I) or no pure-strategy equilibrium (Class II), and which also has a Pareto-optimal non-Nash “cooperative outcome,” P can induce this outcome if p is sufficiently high. This scenario helps to explain the observed outcomes of a Class I game modeling the 1962 Cuban missile crisis between the United States and the Soviet Union, and a Class II game modeling the 2015 conflict between Iran and Israel over Iran’s possible development of nuclear weapons.

Stabilizing Unstable Outcomes in Prediction Games