| Summary: | We present a model of boundedly rational play in single-shot 2 × 2 games. Players choose strategies based on the perceived salience of their own payoffs and, if own-payoff salience is uninformative, on the perceived salience of their opponent’s payoffs. When own payoffs are salient, the model’s predictions correspond to those of Level-1 players in a cognitive hierarchy model. When it is the other player’s payoffs that are salient, the predictions of the model correspond to those of traditional game theory. The model provides unique predictions for the entire class of 2 × 2 games. It identifies games where a Nash equilibrium will always occur, ones where it will never occur, and ones where it will occur only for certain payoff values. It also predicts the outcome of games for which there are no pure Nash equilibria. Experimental results supporting these predictions are presented.
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