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International Journal of Game Theory最新文献

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Exact asymptotics and continuous approximations for the Lowest Unique Positive Integer game 最小唯一正整数对策的精确渐近和连续逼近
IF 0.6 4区 经济学
International Journal of Game Theory Pub Date : 2023-11-20 DOI: 10.1007/s00182-023-00881-0
Arvind Srinivasan, Burton Simon
{"title":"Exact asymptotics and continuous approximations for the Lowest Unique Positive Integer game","authors":"Arvind Srinivasan, Burton Simon","doi":"10.1007/s00182-023-00881-0","DOIUrl":"https://doi.org/10.1007/s00182-023-00881-0","url":null,"abstract":"<p>The Lowest Unique Positive Integer game, a.k.a. Limbo, is among the simplest games that can be played by any number of players and has a nontrivial strategic component. Players independently pick positive integers, and the winner is the player that picks the smallest number nobody else picks. The Nash equilibrium for this game is a mixed strategy, <span>((p(1),p(2),ldots ))</span>, where <i>p</i>(<i>k</i>) is the probability you pick <i>k</i>. A recursion for the Nash equilibrium has been previously worked out in the case where the number of players is Poisson distributed, an assumption that can be justified when there is a large pool of potential players. Here, we summarize previous results and prove that as the (expected) number of players, <i>n</i>, goes to infinity, a properly scaled version of the Nash equilibrium random variable converges in distribution to a Unif(0, 1) random variable. The result implies that for large <i>n</i>, players should choose a number uniformly between 1 and <span>(phi _n sim O(n/ln (n)))</span>. Convergence to the uniform is rather slow, so we also investigate a continuous analog of the Nash equilibrium using a differential equation derived from the recursion. The resulting approximation is unexpectedly accurate and is interesting in its own right. Studying the differential equation yields some useful analytical results, including a precise expression for <span>(phi _n)</span>, and efficient ways to sample from the continuous approximation.</p>","PeriodicalId":14155,"journal":{"name":"International Journal of Game Theory","volume":"7 4","pages":""},"PeriodicalIF":0.6,"publicationDate":"2023-11-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138494998","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"经济学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Coalition-weighted Shapley values 联盟加权沙普利值
4区 经济学
International Journal of Game Theory Pub Date : 2023-11-07 DOI: 10.1007/s00182-023-00877-w
Estela Sánchez-Rodríguez, Miguel Ángel Mirás Calvo, Carmen Quinteiro Sandomingo, Iago Núñez Lugilde
{"title":"Coalition-weighted Shapley values","authors":"Estela Sánchez-Rodríguez, Miguel Ángel Mirás Calvo, Carmen Quinteiro Sandomingo, Iago Núñez Lugilde","doi":"10.1007/s00182-023-00877-w","DOIUrl":"https://doi.org/10.1007/s00182-023-00877-w","url":null,"abstract":"","PeriodicalId":14155,"journal":{"name":"International Journal of Game Theory","volume":"34 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-11-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135480166","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"经济学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Winning strategies of (i, j) multimove games on Thai, Japanese, and Chinese chess games 在泰国、日本和中国象棋比赛中(i, j)多步棋的获胜策略
4区 经济学
International Journal of Game Theory Pub Date : 2023-11-07 DOI: 10.1007/s00182-023-00880-1
Tanayot Prapaithrakul, Saharath Sanguanpong, Nantapath Trakultraipruk
{"title":"Winning strategies of (i, j) multimove games on Thai, Japanese, and Chinese chess games","authors":"Tanayot Prapaithrakul, Saharath Sanguanpong, Nantapath Trakultraipruk","doi":"10.1007/s00182-023-00880-1","DOIUrl":"https://doi.org/10.1007/s00182-023-00880-1","url":null,"abstract":"","PeriodicalId":14155,"journal":{"name":"International Journal of Game Theory","volume":"238 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-11-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135476225","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"经济学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Full disclosure in competitive Bayesian persuasion 竞争贝叶斯说服中的充分披露
4区 经济学
International Journal of Game Theory Pub Date : 2023-10-11 DOI: 10.1007/s00182-023-00873-0
Quan Li, Kang Rong
{"title":"Full disclosure in competitive Bayesian persuasion","authors":"Quan Li, Kang Rong","doi":"10.1007/s00182-023-00873-0","DOIUrl":"https://doi.org/10.1007/s00182-023-00873-0","url":null,"abstract":"","PeriodicalId":14155,"journal":{"name":"International Journal of Game Theory","volume":"28 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136062477","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"经济学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Professor Stef Tijs (1937–2023) 斯蒂夫-蒂斯教授（1937-2023）
4区 经济学
International Journal of Game Theory Pub Date : 2023-10-11 DOI: 10.1007/s00182-023-00876-x
Peter Borm, Hans Peters
{"title":"Professor Stef Tijs (1937–2023)","authors":"Peter Borm, Hans Peters","doi":"10.1007/s00182-023-00876-x","DOIUrl":"https://doi.org/10.1007/s00182-023-00876-x","url":null,"abstract":"","PeriodicalId":14155,"journal":{"name":"International Journal of Game Theory","volume":"122 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136208787","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"经济学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
A characterization of consistent assessments using power sequences of strategy profiles 利用战略概况的权力序列对一致性评估进行表征
4区 经济学
International Journal of Game Theory Pub Date : 2023-10-11 DOI: 10.1007/s00182-023-00874-z
Francesc Dilmé
{"title":"A characterization of consistent assessments using power sequences of strategy profiles","authors":"Francesc Dilmé","doi":"10.1007/s00182-023-00874-z","DOIUrl":"https://doi.org/10.1007/s00182-023-00874-z","url":null,"abstract":"Abstract This paper provides a new characterization of belief consistency in extensive games. We show that all consistent assessments are supported by sequences of strategy profiles with the property that all actions with vanishing probability are played according to power functions of the sequence index. The result makes it simpler to prove or disprove that a given assessment is consistent, facilitating the use of sequential equilibria.","PeriodicalId":14155,"journal":{"name":"International Journal of Game Theory","volume":"7 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136062439","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"经济学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
A note on the risk dominance of the Nash demand game 关于纳什需求博弈的风险优势
4区 经济学
International Journal of Game Theory Pub Date : 2023-10-10 DOI: 10.1007/s00182-023-00872-1
Yoshio Kamijo
{"title":"A note on the risk dominance of the Nash demand game","authors":"Yoshio Kamijo","doi":"10.1007/s00182-023-00872-1","DOIUrl":"https://doi.org/10.1007/s00182-023-00872-1","url":null,"abstract":"","PeriodicalId":14155,"journal":{"name":"International Journal of Game Theory","volume":"3 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136295450","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"经济学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Deterministic n-person shortest path and terminal games on symmetric digraphs have Nash equilibria in pure stationary strategies 对称有向图上的确定性n人最短路径和终端对策在纯平稳策略下具有纳什均衡
4区 经济学
International Journal of Game Theory Pub Date : 2023-10-10 DOI: 10.1007/s00182-023-00875-y
Endre Boros, Paolo Giulio Franciosa, Vladimir Gurvich, Michael Vyalyi
{"title":"Deterministic n-person shortest path and terminal games on symmetric digraphs have Nash equilibria in pure stationary strategies","authors":"Endre Boros, Paolo Giulio Franciosa, Vladimir Gurvich, Michael Vyalyi","doi":"10.1007/s00182-023-00875-y","DOIUrl":"https://doi.org/10.1007/s00182-023-00875-y","url":null,"abstract":"Abstract We prove that a deterministic n -person shortest path game has a Nash equlibrium in pure and stationary strategies if it is edge-symmetric (that is ( u , v ) is a move whenever ( v , u ) is, apart from moves entering terminal vertices) and the length of every move is positive for each player. Both conditions are essential, though it remains an open problem whether there exists a NE-free 2-person non-edge-symmetric game with positive lengths. We provide examples for NE-free 2-person edge-symmetric games that are not positive. We also consider the special case of terminal games (shortest path games in which only terminal moves have nonzero length, possibly negative) and prove that edge-symmetric n -person terminal games always have Nash equilibria in pure and stationary strategies. Furthermore, we prove that an edge-symmetric 2-person terminal game has a uniform (subgame perfect) Nash equilibrium, provided any infinite play is worse than any of the terminals for both players.","PeriodicalId":14155,"journal":{"name":"International Journal of Game Theory","volume":"74 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136295452","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"经济学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 2
Evolution of preferences in multiple populations 多种人群偏好的演变
IF 0.6 4区 经济学
International Journal of Game Theory Pub Date : 2023-09-07 DOI: 10.1007/s00182-023-00869-w
Yu-Sung Tu, Wei-Torng Juang
{"title":"Evolution of preferences in multiple populations","authors":"Yu-Sung Tu, Wei-Torng Juang","doi":"10.1007/s00182-023-00869-w","DOIUrl":"https://doi.org/10.1007/s00182-023-00869-w","url":null,"abstract":"","PeriodicalId":14155,"journal":{"name":"International Journal of Game Theory","volume":" ","pages":""},"PeriodicalIF":0.6,"publicationDate":"2023-09-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45982337","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"经济学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Best-response equilibrium: an equilibrium in finitely additive mixed strategies 最佳响应均衡：有限加性混合策略中的一个均衡
IF 0.6 4区 经济学
International Journal of Game Theory Pub Date : 2023-08-31 DOI: 10.1007/s00182-023-00871-2
Igal Milchtaich
{"title":"Best-response equilibrium: an equilibrium in finitely additive mixed strategies","authors":"Igal Milchtaich","doi":"10.1007/s00182-023-00871-2","DOIUrl":"https://doi.org/10.1007/s00182-023-00871-2","url":null,"abstract":"","PeriodicalId":14155,"journal":{"name":"International Journal of Game Theory","volume":" ","pages":""},"PeriodicalIF":0.6,"publicationDate":"2023-08-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49256713","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"经济学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 1
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