Average behavior in learning models

Abstract We examine a general class of adaptive behavior models in which the distant past has only a weak effect on current actions, and assume that agents sometimes make mistakes, to show that average behavior (averaged over time) converges, with probability one, to a unique limit. Mistakes generate global convergence and are an equilibrium selection device; for small mistake probabilities the equilibrium selected is close to an equilibrium of the model without mistakes. The overlapping generations model, and learning in games with bounded memory, fit into this framework and are examined as examples of the result.

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