The evolution of rationality and the Red Queen

Strategic rationality is subjected here to natural selection. In a zero-sum repeated game of incomplete information, one long-run individual is informed of the state of the world, and plays against a sequence of short-run opponents who are not. Strategies are noisy and have bounded recall. An equilibrium in these is shown to exist. Relative to any such equilibrium, sufficiently greater recall enjoys an advantage that is not decreasing in the original level of recall, thus capturing the Red Queen effect. The selection pressure to reduce a small amount of noise is less than that to increase recall.