Manuel A. Torres-Gomar, Rolando Cavazos-Cadena, Hugo Cruz-Suárez
{"title":"具有风险敏感总奖励标准的可数马尔可夫停止博弈","authors":"Manuel A. Torres-Gomar, Rolando Cavazos-Cadena, Hugo Cruz-Suárez","doi":"10.14736/kyb-2024-1-0001","DOIUrl":null,"url":null,"abstract":"This paper studies Markov stopping games with two players on a denumerable state space. At each decision time player II has two actions: to stop the game paying a terminal reward to player I, or to let the system to continue it evolution. In this latter case, player I selects an action affecting the transitions and charges a running reward to player II. The performance of each pair of strategies is measured by the risk-sensitive total expected reward of player I. Under mild continuity and compactness conditions on the components of the model, it is proved that the value of the game satisfies an equilibrium equation, and the existence of a Nash equilibrium is established.","PeriodicalId":49928,"journal":{"name":"Kybernetika","volume":null,"pages":null},"PeriodicalIF":0.9000,"publicationDate":"2024-04-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Denumerable Markov stopping games with risk-sensitive total reward criterion\",\"authors\":\"Manuel A. Torres-Gomar, Rolando Cavazos-Cadena, Hugo Cruz-Suárez\",\"doi\":\"10.14736/kyb-2024-1-0001\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"This paper studies Markov stopping games with two players on a denumerable state space. At each decision time player II has two actions: to stop the game paying a terminal reward to player I, or to let the system to continue it evolution. In this latter case, player I selects an action affecting the transitions and charges a running reward to player II. The performance of each pair of strategies is measured by the risk-sensitive total expected reward of player I. Under mild continuity and compactness conditions on the components of the model, it is proved that the value of the game satisfies an equilibrium equation, and the existence of a Nash equilibrium is established.\",\"PeriodicalId\":49928,\"journal\":{\"name\":\"Kybernetika\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.9000,\"publicationDate\":\"2024-04-08\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Kybernetika\",\"FirstCategoryId\":\"94\",\"ListUrlMain\":\"https://doi.org/10.14736/kyb-2024-1-0001\",\"RegionNum\":4,\"RegionCategory\":\"计算机科学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q4\",\"JCRName\":\"COMPUTER SCIENCE, CYBERNETICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Kybernetika","FirstCategoryId":"94","ListUrlMain":"https://doi.org/10.14736/kyb-2024-1-0001","RegionNum":4,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"COMPUTER SCIENCE, CYBERNETICS","Score":null,"Total":0}
引用次数: 0
摘要
本文研究的是可数状态空间上有两个玩家的马尔可夫停止博弈。在每个决策时间,玩家 II 有两个行动:停止博弈并向玩家 I 支付终结奖励,或让系统继续演化。在后一种情况下,玩家 I 选择一个影响过渡的行动,并向玩家 II 支付运行奖励。每对策略的表现都以棋手 I 对风险敏感的总预期报酬来衡量。在模型各组成部分的温和连续性和紧凑性条件下,证明了博弈值满足均衡方程,并确定了纳什均衡的存在。
Denumerable Markov stopping games with risk-sensitive total reward criterion
This paper studies Markov stopping games with two players on a denumerable state space. At each decision time player II has two actions: to stop the game paying a terminal reward to player I, or to let the system to continue it evolution. In this latter case, player I selects an action affecting the transitions and charges a running reward to player II. The performance of each pair of strategies is measured by the risk-sensitive total expected reward of player I. Under mild continuity and compactness conditions on the components of the model, it is proved that the value of the game satisfies an equilibrium equation, and the existence of a Nash equilibrium is established.
期刊介绍:
Kybernetika is the bi-monthly international journal dedicated for rapid publication of high-quality, peer-reviewed research articles in fields covered by its title. The journal is published by Nakladatelství Academia, Centre of Administration and Operations of the Czech Academy of Sciences for the Institute of Information Theory and Automation of The Czech Academy of Sciences.
Kybernetika traditionally publishes research results in the fields of Control Sciences, Information Sciences, Statistical Decision Making, Applied Probability Theory, Random Processes, Operations Research, Fuzziness and Uncertainty Theories, as well as in the topics closely related to the above fields.