{"title":"无限对策下库恩定理的推广","authors":"Masayuki Takahashi","doi":"10.32917/HMJ/1206138533","DOIUrl":null,"url":null,"abstract":"An extensive ^-person game is usually described in terms of a finite tree in an oriented plane. The game involves in its structure the mixed and behavior strategies of each player closely related to some specified information sets. Under the assumption that each move possesses at least two alternatives, H.W. Kuhn [1] proved the theorem that the game has perfect recall if and only if, given any mixed strategies μu β2, •••, βn, there may be associated with them behavior strategies βu /32, •••, /?», each /?,depending only on the corresponding mixed strategy /*,-, so that they give rise to the equalities,","PeriodicalId":17080,"journal":{"name":"Journal of science of the Hiroshima University Ser. A Mathematics, physics, chemistry","volume":"106 1","pages":"237-242"},"PeriodicalIF":0.0000,"publicationDate":"1969-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"1","resultStr":"{\"title\":\"A generalization of Kuhn's theorem for an infinite game\",\"authors\":\"Masayuki Takahashi\",\"doi\":\"10.32917/HMJ/1206138533\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"An extensive ^-person game is usually described in terms of a finite tree in an oriented plane. The game involves in its structure the mixed and behavior strategies of each player closely related to some specified information sets. Under the assumption that each move possesses at least two alternatives, H.W. Kuhn [1] proved the theorem that the game has perfect recall if and only if, given any mixed strategies μu β2, •••, βn, there may be associated with them behavior strategies βu /32, •••, /?», each /?,depending only on the corresponding mixed strategy /*,-, so that they give rise to the equalities,\",\"PeriodicalId\":17080,\"journal\":{\"name\":\"Journal of science of the Hiroshima University Ser. A Mathematics, physics, chemistry\",\"volume\":\"106 1\",\"pages\":\"237-242\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"1969-01-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"1\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Journal of science of the Hiroshima University Ser. A Mathematics, physics, chemistry\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.32917/HMJ/1206138533\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of science of the Hiroshima University Ser. A Mathematics, physics, chemistry","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.32917/HMJ/1206138533","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
A generalization of Kuhn's theorem for an infinite game
An extensive ^-person game is usually described in terms of a finite tree in an oriented plane. The game involves in its structure the mixed and behavior strategies of each player closely related to some specified information sets. Under the assumption that each move possesses at least two alternatives, H.W. Kuhn [1] proved the theorem that the game has perfect recall if and only if, given any mixed strategies μu β2, •••, βn, there may be associated with them behavior strategies βu /32, •••, /?», each /?,depending only on the corresponding mixed strategy /*,-, so that they give rise to the equalities,