Adaptive learning and p-best response sets
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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Volume (Year): 40 (2011)
Issue (Month): 4 (November)
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