{"title":"Minimally incomplete sampling and convergence of adaptive play in $$2\\times 2$$ games","authors":"","doi":"10.1007/s40505-024-00262-0","DOIUrl":null,"url":null,"abstract":"<h3>Abstract</h3> <p>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 <span> <span>\\(2\\times 2\\)</span> </span> coordination games <em>any</em> 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.</p>","PeriodicalId":40852,"journal":{"name":"Economic Theory Bulletin","volume":"2 1","pages":""},"PeriodicalIF":0.4000,"publicationDate":"2024-04-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Economic Theory Bulletin","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1007/s40505-024-00262-0","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"ECONOMICS","Score":null,"Total":0}
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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.
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.
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