{"title":"Complete conditional type structures","authors":"Nicodemo De Vito","doi":"10.1016/j.geb.2024.10.006","DOIUrl":null,"url":null,"abstract":"<div><div>Hierarchies of conditional beliefs (<span><span>Battigalli and Siniscalchi, 1999</span></span>) play a central role for the epistemic analysis of solution concepts in sequential games. They are modelled by type structures, which allow the analyst to represent the players' hierarchies without specifying an infinite sequence of conditional beliefs. Here, we study type structures that satisfy a “richness” property, called <em>completeness</em>. <span><span>Friedenberg (2010)</span></span> shows that, under specific conditions, a complete type structure with ordinary beliefs represents all hierarchies. This paper shows that Friedenberg's result can be extended to type structures with conditional beliefs. As an ancillary result of independent interest, we provide a construction of the “canonical” space of hierarchies of conditional beliefs which generalizes the one in <span><span>Battigalli and Siniscalchi (1999)</span></span>.</div></div>","PeriodicalId":48291,"journal":{"name":"Games and Economic Behavior","volume":"148 ","pages":"Pages 427-448"},"PeriodicalIF":1.0000,"publicationDate":"2024-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Games and Economic Behavior","FirstCategoryId":"96","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0899825624001520","RegionNum":3,"RegionCategory":"经济学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"ECONOMICS","Score":null,"Total":0}
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Abstract
Hierarchies of conditional beliefs (Battigalli and Siniscalchi, 1999) play a central role for the epistemic analysis of solution concepts in sequential games. They are modelled by type structures, which allow the analyst to represent the players' hierarchies without specifying an infinite sequence of conditional beliefs. Here, we study type structures that satisfy a “richness” property, called completeness. Friedenberg (2010) shows that, under specific conditions, a complete type structure with ordinary beliefs represents all hierarchies. This paper shows that Friedenberg's result can be extended to type structures with conditional beliefs. As an ancillary result of independent interest, we provide a construction of the “canonical” space of hierarchies of conditional beliefs which generalizes the one in Battigalli and Siniscalchi (1999).
期刊介绍：
Games and Economic Behavior facilitates cross-fertilization between theories and applications of game theoretic reasoning. It consistently attracts the best quality and most creative papers in interdisciplinary studies within the social, biological, and mathematical sciences. Most readers recognize it as the leading journal in game theory. Research Areas Include: • Game theory • Economics • Political science • Biology • Computer science • Mathematics • Psychology
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