A theory of focal points in 2 × 2 games

Since the classic work of Schelling, the notion of a focal point has been widely applied to explain coordinated behavior. However, focal points remain largely outside the formal apparatus of game theory. This paper develops a model of play in 2 × 2 games where payoff differences determine what strategy players will perceive as “salient” and choose to play. The model uniquely predicts which outcome will emerge for virtually the entire class of 2 × 2 normal form games. For the subset of such games involving coordination and asymmetric payoffs, payoff differences identify focal outcomes and strategies in the same way shared social knowledge produces coordination in Schelling’s symmetric games. The model characterizes situations when Nash equilibria are likely to be played, even in a one-shot interaction, and predicts which equilibrium will obtain in games containing more than one. It identifies other circumstances in which a non-equilibrium outcome will predominate. Finally, the theory specifies when a player is likely to select a strategy based solely on consideration of her own payoffs, and when and why the same player will be prompted to act strategically. Experimental results are presented that test the predictions of the model.