{"title":"The Population Lotto Game: how strategic resource allocation structures non-transitive outcomes in pairwise competitions","authors":"","doi":"10.1007/s00182-024-00891-6","DOIUrl":null,"url":null,"abstract":"<h3>Abstract</h3> <p>In order to understand if and how strategic resource allocation can constrain the structure of pair-wise competition outcomes in human competitions we introduce a new multiplayer resource allocation game, the Population Lotto Game. This new game allows agents to allocate their resources across a continuum of possible specializations. While this game allows non-transitive cycles between players, we show that the Nash equilibrium of the game also forms a hierarchical structure between discrete ‘leagues’ based on their different resource budgets, with potential sub-league structure and/or non-transitive cycles inside individual leagues. We provide an algorithm that can find a particular Nash equilibrium for any finite set of discrete sub-population sizes and budgets. Further, our algorithm finds the unique Nash equilibrium that remains stable for the subset of players with budgets below any threshold.</p>","PeriodicalId":14155,"journal":{"name":"International Journal of Game Theory","volume":"12 1","pages":""},"PeriodicalIF":0.6000,"publicationDate":"2024-04-03","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/s00182-024-00891-6","RegionNum":4,"RegionCategory":"经济学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"ECONOMICS","Score":null,"Total":0}
引用次数: 0
Abstract
In order to understand if and how strategic resource allocation can constrain the structure of pair-wise competition outcomes in human competitions we introduce a new multiplayer resource allocation game, the Population Lotto Game. This new game allows agents to allocate their resources across a continuum of possible specializations. While this game allows non-transitive cycles between players, we show that the Nash equilibrium of the game also forms a hierarchical structure between discrete ‘leagues’ based on their different resource budgets, with potential sub-league structure and/or non-transitive cycles inside individual leagues. We provide an algorithm that can find a particular Nash equilibrium for any finite set of discrete sub-population sizes and budgets. Further, our algorithm finds the unique Nash equilibrium that remains stable for the subset of players with budgets below any threshold.
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.
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