{"title":"狼人游戏中的最佳策略:博弈论视角","authors":"ST Wang","doi":"arxiv-2408.17177","DOIUrl":null,"url":null,"abstract":"Werewolf game, also known as Mafia game, is a social deduction game that\nmodels the conflict between an informed minority (werewolf group) and an\nuninformed majority (citizen group). This paper explores the optimal strategies\nof the werewolf game from the perspective of game theory, focusing on cases\nboth with and without prophet. First we examine the existing strategy in game\nwithout prophet and propose ``random strategy +\", which provides an improved\nwinning probability for the werewolve group. Then we further study the game\nwith prophet, and find the game with prophet can be transformed into a\nextensive game with complete but imperfect information under a specific rule.\nWe construct a model and design an algorithm to achieve PBE and maximize the\ncitizen group's winning probability. In the end, we examine a property of PBE\nin game without any restriction.","PeriodicalId":501273,"journal":{"name":"arXiv - ECON - General Economics","volume":"41 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2024-08-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Optimal Strategy in Werewolf Game: A Game Theoretic Perspective\",\"authors\":\"ST Wang\",\"doi\":\"arxiv-2408.17177\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Werewolf game, also known as Mafia game, is a social deduction game that\\nmodels the conflict between an informed minority (werewolf group) and an\\nuninformed majority (citizen group). This paper explores the optimal strategies\\nof the werewolf game from the perspective of game theory, focusing on cases\\nboth with and without prophet. First we examine the existing strategy in game\\nwithout prophet and propose ``random strategy +\\\", which provides an improved\\nwinning probability for the werewolve group. Then we further study the game\\nwith prophet, and find the game with prophet can be transformed into a\\nextensive game with complete but imperfect information under a specific rule.\\nWe construct a model and design an algorithm to achieve PBE and maximize the\\ncitizen group's winning probability. In the end, we examine a property of PBE\\nin game without any restriction.\",\"PeriodicalId\":501273,\"journal\":{\"name\":\"arXiv - ECON - General Economics\",\"volume\":\"41 1\",\"pages\":\"\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2024-08-30\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"arXiv - ECON - General Economics\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/arxiv-2408.17177\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"arXiv - ECON - General Economics","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/arxiv-2408.17177","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
Optimal Strategy in Werewolf Game: A Game Theoretic Perspective
Werewolf game, also known as Mafia game, is a social deduction game that
models the conflict between an informed minority (werewolf group) and an
uninformed majority (citizen group). This paper explores the optimal strategies
of the werewolf game from the perspective of game theory, focusing on cases
both with and without prophet. First we examine the existing strategy in game
without prophet and propose ``random strategy +", which provides an improved
winning probability for the werewolve group. Then we further study the game
with prophet, and find the game with prophet can be transformed into a
extensive game with complete but imperfect information under a specific rule.
We construct a model and design an algorithm to achieve PBE and maximize the
citizen group's winning probability. In the end, we examine a property of PBE
in game without any restriction.