Does Rational Learning Lead to Nash Equilibrium in Finitely Repeated Games?

A stage game is played for many periods. Each player maximizes discounted expected payoffs, given updated beliefs about opponent's strategies. For the case of infinitely repeated games, Kalai and Lehrer [8, 9] show that, under absolute continuity, rational learning leads to Nash equilibrium. Absolute continuity, however, does not ensure convergence to approximate Nash equilibrium play in games of long (but finite) horizon. I show that asymptotic continuity is equivalent to absolute continuity in infinitely repeated games and ensures convergence to Nash equilibrium in finite horizon games. These results unify the learning theory in finitely and infinitely repeated games.Journal of Economic LiteratureClassification Number: D83 Learning.