## 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

Zbl 0773.90101
Full Text:

### References:

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