Normative game theory unsatisfactorily explains rational behavior. Real people do not behave as predicted, and what is prescribed as rational behavior is normally unattainable in real-life. The problem is that current normative analysis does not account for people's cognitive limitations – their bounded rationality. However, this paper develops an account of bounded rationality that explains the rationality of more realistic behavior. I focus on the Centipede Game, in which boundedly rational players explore and test others' immediate behavior, until they can (...) apply limited backward induction. The result is that the game has a solution in the form of a subjective Nash equilibrium, which boundedly rational players can possibly realize. (shrink)