Adaptive learning and p-best response sets

Jacques Durieu (), Philippe Solal and Olivier Tercieux
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Jacques Durieu: CREG - Centre de recherche en économie de Grenoble - UPMF - Université Pierre Mendès France - Grenoble 2

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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, ). 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.

Keywords: fictitious play process; stochastic stability; game theory; evolutionary game theory; théorie des jeux; économie expérimentale (search for similar items in EconPapers)
Date: 2011
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Citations: View citations in EconPapers (13)

Published in International Journal of Game Theory, 2011, 40 (4), pp.735-747

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Journal Article: Adaptive learning and p-best response sets (2011)
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Persistent link: https://EconPapers.repec.org/RePEc:hal:journl:halshs-00740164

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