Abstract

Adaptive learning explains how conventions emerge in populations in which players sample a sufficiently small portion of the recent plays and best reply to those samples. We establish that in \(2\times 2\) coordination games any degree of incomplete sampling is sufficient for a convention to be established and that the degree of sampling does not affect which conventions are most likely to emerge in the long run. Thus, the bound that players sample at most half of the plays available to them, which is prevalent in the large body of work that uses adaptive learning to examine which conventions emerge in a variety of games, is unnecessarily strict.

中文翻译：

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$$2\times 2$$ 游戏中自适应游戏的最小不完全采样和收敛

摘要

适应性学习解释了惯例是如何在群体中出现的，其中玩家对最近的游戏中的一小部分进行采样，并对这些样本做出最佳回应。我们确定，在\(2\times 2\)协调博弈中，任何程度的不完全采样都足以建立约定，并且采样程度不会影响从长远来看哪些约定最有可能出现。因此，玩家最多只能选择一半的游戏，这在使用自适应学习来检查各种游戏中出现的惯例的大量工作中很普遍，这种限制是不必要的严格。