{"title":"Foundation and identification of multi-attribute Shannon entropy","authors":"David Walker-Jones","doi":"10.1016/j.geb.2025.01.006","DOIUrl":null,"url":null,"abstract":"<div><div>By weakening Shannon's original axioms to allow for attributes of the choice environment to differ in their associated learning costs, this paper provides an axiomatic foundation for Multi-Attribute Shannon Entropy, a natural multi-parameter generalization of Shannon Entropy. Sufficient conditions are also provided for a simple dataset that provides a closed-form solution for the Multi-Attribute Shannon Entropy cost function for information by analyzing stochastic choice data produced by a rationally inattentive agent that is picking between pairs of options when relatively few states of the world have a positive probability of being realized.</div></div>","PeriodicalId":48291,"journal":{"name":"Games and Economic Behavior","volume":"150 ","pages":"Pages 334-355"},"PeriodicalIF":1.0000,"publicationDate":"2025-03-01","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/S0899825625000077","RegionNum":3,"RegionCategory":"经济学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"2025/1/31 0:00:00","PubModel":"Epub","JCR":"Q3","JCRName":"ECONOMICS","Score":null,"Total":0}
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Abstract
By weakening Shannon's original axioms to allow for attributes of the choice environment to differ in their associated learning costs, this paper provides an axiomatic foundation for Multi-Attribute Shannon Entropy, a natural multi-parameter generalization of Shannon Entropy. Sufficient conditions are also provided for a simple dataset that provides a closed-form solution for the Multi-Attribute Shannon Entropy cost function for information by analyzing stochastic choice data produced by a rationally inattentive agent that is picking between pairs of options when relatively few states of the world have a positive probability of being realized.
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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