Learning with Hazy Beliefs
Players are rational if they always choose best replies given their beliefs. They are good predictors if the difference between their beliefs and the distribution of the others' actual strategies goes to zero over time. Learning is deterministic if beliefs are fully determined by the initial conditions and the observed data. (Bayesian updating is a particular example). If players are rational, good predictors, and learn deterministically, there are many games for which neither beliefs nor actions converge to a Nash equilibrium. We introduce an alternative approach to learning called prospecting in which players are rational and good predictors, but beliefs have a small random component. In any finite game, and from any initial conditions, prospecting players learn to play arbitrarily close to Nash equilibrium with probability one.
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