Pierre de Callataÿ, Ana Mauleon, Vincent Vannetelbosch
{"title":"远视不稳定性最小","authors":"Pierre de Callataÿ, Ana Mauleon, Vincent Vannetelbosch","doi":"10.1007/s00182-024-00887-2","DOIUrl":null,"url":null,"abstract":"<p>We propose the notion of minimal farsighted instability to determine the states that are more likely to emerge in the long run when agents are farsighted. A state is minimally farsighted unstable if there is no other state which is more farsightedly stable. To formulate what it means to be more farsightedly stable, we compare states by comparing (in the set inclusion or cardinal sense) their sets of farsighted defeating states. We next compare states in terms of their absorbtiveness by comparing both their sets of farsighted defeating states (i.e. in terms of their stability) and their sets of farsighted defeated states (i.e. in terms of their reachability). A state is maximally farsighted absorbing if there is no other state which is more farsightedly absorbing. We provide general results for characterizing minimally farsighted unstable states and maximally farsighted absorbing states, and we study their relationships with alternative notions of farsightedness. Finally, we use experimental data to show the relevance of the new solution concepts.</p>","PeriodicalId":14155,"journal":{"name":"International Journal of Game Theory","volume":"52 1","pages":""},"PeriodicalIF":0.6000,"publicationDate":"2024-03-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Minimal farsighted instability\",\"authors\":\"Pierre de Callataÿ, Ana Mauleon, Vincent Vannetelbosch\",\"doi\":\"10.1007/s00182-024-00887-2\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<p>We propose the notion of minimal farsighted instability to determine the states that are more likely to emerge in the long run when agents are farsighted. A state is minimally farsighted unstable if there is no other state which is more farsightedly stable. To formulate what it means to be more farsightedly stable, we compare states by comparing (in the set inclusion or cardinal sense) their sets of farsighted defeating states. We next compare states in terms of their absorbtiveness by comparing both their sets of farsighted defeating states (i.e. in terms of their stability) and their sets of farsighted defeated states (i.e. in terms of their reachability). A state is maximally farsighted absorbing if there is no other state which is more farsightedly absorbing. We provide general results for characterizing minimally farsighted unstable states and maximally farsighted absorbing states, and we study their relationships with alternative notions of farsightedness. Finally, we use experimental data to show the relevance of the new solution concepts.</p>\",\"PeriodicalId\":14155,\"journal\":{\"name\":\"International Journal of Game Theory\",\"volume\":\"52 1\",\"pages\":\"\"},\"PeriodicalIF\":0.6000,\"publicationDate\":\"2024-03-10\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"International Journal of Game Theory\",\"FirstCategoryId\":\"96\",\"ListUrlMain\":\"https://doi.org/10.1007/s00182-024-00887-2\",\"RegionNum\":4,\"RegionCategory\":\"经济学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q4\",\"JCRName\":\"ECONOMICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"International Journal of Game Theory","FirstCategoryId":"96","ListUrlMain":"https://doi.org/10.1007/s00182-024-00887-2","RegionNum":4,"RegionCategory":"经济学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"ECONOMICS","Score":null,"Total":0}
We propose the notion of minimal farsighted instability to determine the states that are more likely to emerge in the long run when agents are farsighted. A state is minimally farsighted unstable if there is no other state which is more farsightedly stable. To formulate what it means to be more farsightedly stable, we compare states by comparing (in the set inclusion or cardinal sense) their sets of farsighted defeating states. We next compare states in terms of their absorbtiveness by comparing both their sets of farsighted defeating states (i.e. in terms of their stability) and their sets of farsighted defeated states (i.e. in terms of their reachability). A state is maximally farsighted absorbing if there is no other state which is more farsightedly absorbing. We provide general results for characterizing minimally farsighted unstable states and maximally farsighted absorbing states, and we study their relationships with alternative notions of farsightedness. Finally, we use experimental data to show the relevance of the new solution concepts.
期刊介绍:
International Journal of Game Theory is devoted to game theory and its applications. It publishes original research making significant contributions from a methodological, conceptual or mathematical point of view. Survey articles may also be considered if especially useful for the field.