{"title":"The three-player lowest unique number game","authors":"Balázs Sentes","doi":"10.1016/j.econlet.2025.112299","DOIUrl":null,"url":null,"abstract":"<div><div>This paper characterizes the unique symmetric mixed-strategy Nash equilibrium in the three-player version Lowest Unique Number Game. In this game, each player chooses a positive integer simultaneously and the player with the lowest unique number wins. The equilibrium mixing is shown to have full support and it is characterized by a constant hazard rate which is around <span><math><mrow><mo>.</mo><mn>46</mn></mrow></math></span>.</div></div>","PeriodicalId":11468,"journal":{"name":"Economics Letters","volume":"251 ","pages":"Article 112299"},"PeriodicalIF":1.8000,"publicationDate":"2025-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Economics Letters","FirstCategoryId":"96","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0165176525001363","RegionNum":4,"RegionCategory":"经济学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"2025/3/28 0:00:00","PubModel":"Epub","JCR":"Q2","JCRName":"ECONOMICS","Score":null,"Total":0}
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Abstract
This paper characterizes the unique symmetric mixed-strategy Nash equilibrium in the three-player version Lowest Unique Number Game. In this game, each player chooses a positive integer simultaneously and the player with the lowest unique number wins. The equilibrium mixing is shown to have full support and it is characterized by a constant hazard rate which is around .
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