{"title":"用优势启发式计算双矩阵对策的均衡","authors":"R. Aras, A. Dutech, F. Charpillet","doi":"10.1109/ICTAI.2006.44","DOIUrl":null,"url":null,"abstract":"We propose a formulation of a general-sum bimatrix game as a bipartite directed graph with the objective of establishing a correspondence between the set of the relevant structures of the graph (in particular elementary cycles) and the set of the Nash equilibria of the game. We show that finding the set of elementary cycles of the graph permits the computation of the set of equilibria. For games whose graphs have a sparse adjacency matrix, this serves as a good heuristic for computing the set of equilibria. The heuristic also allows the discarding of sections of the support space that do not yield any equilibrium, thus serving as a useful preprocessing step for algorithms that compute the equilibria through support enumeration","PeriodicalId":169424,"journal":{"name":"2006 18th IEEE International Conference on Tools with Artificial Intelligence (ICTAI'06)","volume":"17 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2006-11-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"3","resultStr":"{\"title\":\"Computing the Equilibria of Bimatrix Games Using Dominance Heuristics\",\"authors\":\"R. Aras, A. Dutech, F. Charpillet\",\"doi\":\"10.1109/ICTAI.2006.44\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"We propose a formulation of a general-sum bimatrix game as a bipartite directed graph with the objective of establishing a correspondence between the set of the relevant structures of the graph (in particular elementary cycles) and the set of the Nash equilibria of the game. We show that finding the set of elementary cycles of the graph permits the computation of the set of equilibria. For games whose graphs have a sparse adjacency matrix, this serves as a good heuristic for computing the set of equilibria. The heuristic also allows the discarding of sections of the support space that do not yield any equilibrium, thus serving as a useful preprocessing step for algorithms that compute the equilibria through support enumeration\",\"PeriodicalId\":169424,\"journal\":{\"name\":\"2006 18th IEEE International Conference on Tools with Artificial Intelligence (ICTAI'06)\",\"volume\":\"17 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2006-11-13\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"3\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"2006 18th IEEE International Conference on Tools with Artificial Intelligence (ICTAI'06)\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1109/ICTAI.2006.44\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"2006 18th IEEE International Conference on Tools with Artificial Intelligence (ICTAI'06)","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1109/ICTAI.2006.44","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
Computing the Equilibria of Bimatrix Games Using Dominance Heuristics
We propose a formulation of a general-sum bimatrix game as a bipartite directed graph with the objective of establishing a correspondence between the set of the relevant structures of the graph (in particular elementary cycles) and the set of the Nash equilibria of the game. We show that finding the set of elementary cycles of the graph permits the computation of the set of equilibria. For games whose graphs have a sparse adjacency matrix, this serves as a good heuristic for computing the set of equilibria. The heuristic also allows the discarding of sections of the support space that do not yield any equilibrium, thus serving as a useful preprocessing step for algorithms that compute the equilibria through support enumeration