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Article Dans Une Revue International Journal of Game Theory Année : 2011

Adaptive learning and p-best response sets

Résumé

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.
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Dates et versions

halshs-00740164 , version 1 (09-10-2012)

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  • HAL Id : halshs-00740164 , version 1
  • PRODINRA : 244412

Citer

Jacques Durieu, Philippe Solal, Olivier Tercieux. Adaptive learning and p-best response sets. International Journal of Game Theory, 2011, 40 (4), pp.735-747. ⟨halshs-00740164⟩
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