{"title":"论基于状态的潜在博弈的等价性","authors":"Han Wu, Jinhuan Wang","doi":"10.1007/s11432-023-3995-5","DOIUrl":null,"url":null,"abstract":"<p>In this paper, we explore state-based potential games using the semi-tensor product of matrices. First, applying the potential equation, we derive both a necessary and sufficient condition as well as a sufficient condition to verify whether a state-based game qualifies as a potential game. Next, we present two static equivalence conditions of state-based potential games. We then delve into dynamic equivalence. We propose a criterion that allows us to identify state-based games that are dynamically equivalent to state-based potential games and share similar dynamic properties. Ultimately, we introduce the concept of state-based networked evolutionary games. We provide a necessary and sufficient condition to ensure that a state-based networked evolutionary game can be classified as a state-based potential game.</p>","PeriodicalId":21618,"journal":{"name":"Science China Information Sciences","volume":"39 1","pages":""},"PeriodicalIF":7.3000,"publicationDate":"2024-05-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"On equivalence of state-based potential games\",\"authors\":\"Han Wu, Jinhuan Wang\",\"doi\":\"10.1007/s11432-023-3995-5\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<p>In this paper, we explore state-based potential games using the semi-tensor product of matrices. First, applying the potential equation, we derive both a necessary and sufficient condition as well as a sufficient condition to verify whether a state-based game qualifies as a potential game. Next, we present two static equivalence conditions of state-based potential games. We then delve into dynamic equivalence. We propose a criterion that allows us to identify state-based games that are dynamically equivalent to state-based potential games and share similar dynamic properties. Ultimately, we introduce the concept of state-based networked evolutionary games. We provide a necessary and sufficient condition to ensure that a state-based networked evolutionary game can be classified as a state-based potential game.</p>\",\"PeriodicalId\":21618,\"journal\":{\"name\":\"Science China Information Sciences\",\"volume\":\"39 1\",\"pages\":\"\"},\"PeriodicalIF\":7.3000,\"publicationDate\":\"2024-05-15\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Science China Information Sciences\",\"FirstCategoryId\":\"94\",\"ListUrlMain\":\"https://doi.org/10.1007/s11432-023-3995-5\",\"RegionNum\":2,\"RegionCategory\":\"计算机科学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q1\",\"JCRName\":\"COMPUTER SCIENCE, INFORMATION SYSTEMS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Science China Information Sciences","FirstCategoryId":"94","ListUrlMain":"https://doi.org/10.1007/s11432-023-3995-5","RegionNum":2,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"COMPUTER SCIENCE, INFORMATION SYSTEMS","Score":null,"Total":0}
In this paper, we explore state-based potential games using the semi-tensor product of matrices. First, applying the potential equation, we derive both a necessary and sufficient condition as well as a sufficient condition to verify whether a state-based game qualifies as a potential game. Next, we present two static equivalence conditions of state-based potential games. We then delve into dynamic equivalence. We propose a criterion that allows us to identify state-based games that are dynamically equivalent to state-based potential games and share similar dynamic properties. Ultimately, we introduce the concept of state-based networked evolutionary games. We provide a necessary and sufficient condition to ensure that a state-based networked evolutionary game can be classified as a state-based potential game.
期刊介绍:
Science China Information Sciences is a dedicated journal that showcases high-quality, original research across various domains of information sciences. It encompasses Computer Science & Technologies, Control Science & Engineering, Information & Communication Engineering, Microelectronics & Solid-State Electronics, and Quantum Information, providing a platform for the dissemination of significant contributions in these fields.