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Adaptive learning and \(p\)-best response sets. (English) Zbl 1233.91035

Summary: A product set of strategies is a \(p\)-best response set if for each agent it contains all best responses to any distribution placing at least probability \(p\) on his opponents’ profiles belonging to the product set. A \(p\)-best response set is minimal if it does not properly contain another \(p\)-best response set. We study a perturbed joint fictitious play process with bounded memory and sample and a perturbed independent fictitious play process as in [H. P. Young, Econometrica 61, No. 1, 57–84 (1993; Zbl 0773.90101)]. We show that in \(n\)-person games only strategies contained in the unique minimal \(p\)-best response set can be selected in the long run by both types of processes provided that the rate of perturbations and \(p\) are sufficiently low. For each process, an explicit bound of \(p\) is given and we analyze how this critical value evolves when \(n\) increases. Our results are robust to the degree of incompleteness of sampling relative to memory.

MSC:

91A22 Evolutionary games
91A26 Rationality and learning in game theory

Citations:

Zbl 0773.90101
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References:

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