{"title":"A Short Proof of Reny's Existence Theorem for Payoff Secure Games","authors":"Pavlo Prokopovych","doi":"10.2139/ssrn.1325191","DOIUrl":null,"url":null,"abstract":"A short proof of Reny (1999)'s equilibrium existence theorem for payoff secure games is provided. At the heart of the proof lies the concept of a multivalued mapping with the local intersection property. By means of the Fan-Browder collective fixed-point theorem, we show an approximate equilibrium existence theorem which covers a number of known games. Reny's theorem follows from it straightforwardly.","PeriodicalId":369373,"journal":{"name":"Epistemology eJournal","volume":"86 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2009-01-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"1","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Epistemology eJournal","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.2139/ssrn.1325191","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 1
Abstract
A short proof of Reny (1999)'s equilibrium existence theorem for payoff secure games is provided. At the heart of the proof lies the concept of a multivalued mapping with the local intersection property. By means of the Fan-Browder collective fixed-point theorem, we show an approximate equilibrium existence theorem which covers a number of known games. Reny's theorem follows from it straightforwardly.
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