In a big uncertain game a stage game is played repeatedly by a large anonymous population. Players' privately known types are correlated through an unknown state of fundamentals and the game is played with imperfect monitoring. Under simple behavioral assumptions, the game admits myopic Markov-perfect equilibria. We show that with time, equilibrium play in these games becomes highly predictable and stable, if uncertainty that is not explained by fundamentals is small. Examples include congestion games, markets and adaptation of new technology. (Joint work with Eran Shmaya.)

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