When can rational players learn to play Nash equilibrium starting from out‐of‐equilibrium conditions?
The “classical” case
- The number of players is small
- The rules are common knowledge
- The payoffs, or at least the distribution of possible payoffs, is common knowledge
- Everyone is rational
Even in this high rationality world, learning is difficult because it is interactive: each player’s learning process complicates what has to be learned by everyone else.
Kalai and Lehrer, Econ, 1993 Jordan, GEB, 1991, 1993 Nachbar, Econ, 1997, 2005
In fact, the learning behavior of a Bayesian rational agent can be so complex that it is essentially unlearnable by other rational players.
There are simple games of incomplete information (e.g., matching pennies with uncertain payoffs) such that, for any prior beliefs, Bayesian rational players will fail to come close to Nash equilibrium play with probability one.
Furthermore at least one of the players will almost surely fail to learn how to predict the behavior of his opponent even approximately.
Foster and Young, Proceedings of the National Academy of Sciences, vol. 98, 2001.
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