Minimally incomplete sampling and convergence of adaptive play in $$2\times 2$$ games

IF 0.4 Q4 ECONOMICS

Economic Theory Bulletin Pub Date : 2024-04-04 DOI:10.1007/s40505-024-00262-0

引用次数: 0

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.

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2 次 2$$ 游戏中的最小不完全采样和自适应游戏的收敛性

摘要适应性学习解释了在棋手对最近的棋局进行足够小的抽样并对这些抽样做出最佳回应的群体中，约定是如何出现的。我们发现，在协调博弈中，任何程度的不完全抽样都足以使约定俗成，而且抽样程度并不影响哪些约定俗成从长远来看最有可能出现。因此，关于博弈者最多只能对一半的可用博弈进行抽样的约束是不必要的严格约束，这种约束在大量使用适应性学习来研究各种博弈中哪些约定会出现的研究中非常普遍。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Economic Theory Bulletin ECONOMICS-

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期刊介绍： The purpose of Economic Theory Bulletin is to provide an outlet for research in all areas of Economics based on rigorous theoretical reasoning. The Economic Theory Bulletin together with Economic Theory are the official journals of the Society for the Advancement of Economic Theory. The Economic Theory Bulletin is intended to publish: 1. Short papers/notes of substantial interest. Content is subject to the same standards as Economic Theory: research in all areas of economics based on rigorous theoretical reasoning and on topics in mathematics that are supported by the analysis of economic problems. Published articles contribute to the understanding and solution of substantive economic problems. Theory papers with the substance and style for other journals that specialize in short papers are welcomed. Corollaries of already known results in the literature are not appropriate for publication. 2. Survey papers that clearly picture the basic ideas at work in the area, the essential technical apparatus that is used and the central questions that remain open.