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Adaptive learning and p-best response sets

Abstract

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 Young (Econometrica 61:57–84, 1993). 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.

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Correspondence to O. Tercieux.

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Durieu, J., Solal, P. & Tercieux, O. Adaptive learning and p-best response sets. Int J Game Theory 40, 735–747 (2011). https://doi.org/10.1007/s00182-010-0266-2

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  • DOI: https://doi.org/10.1007/s00182-010-0266-2

Keywords

  • Evolutionary game theory
  • Fictitious play process
  • p-Dominance
  • Stochastic stability

JEL Classification

  • C72
  • C73