{"title":"Positivity of incomplete cooperative games revisited","authors":"Martin Černý","doi":"10.1016/j.orl.2025.107277","DOIUrl":null,"url":null,"abstract":"<div><div>We consider incomplete cooperative games, where only some coalitions' values are specified and others remain indeterminate. Focusing on <em>positive extensions</em>—fully defined cooperative games that agree with the partial data and have nonnegative dividends—we introduce a novel, two-stage dividend-assignment procedure that fully characterizes all such extensions. Our method offers a general criterion for positivity-extendability, introduces an explicit lower bound game, and provides an understanding of the structure of extreme points in the extension set. These contributions significantly expand the toolkit for theoretical analyses and practical computations of incomplete cooperative games, and also shed new light on properties of classical cooperative games.</div></div>","PeriodicalId":54682,"journal":{"name":"Operations Research Letters","volume":"60 ","pages":"Article 107277"},"PeriodicalIF":0.8000,"publicationDate":"2025-03-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Operations Research Letters","FirstCategoryId":"91","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0167637725000380","RegionNum":4,"RegionCategory":"管理学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"OPERATIONS RESEARCH & MANAGEMENT SCIENCE","Score":null,"Total":0}
引用次数: 0
Abstract
We consider incomplete cooperative games, where only some coalitions' values are specified and others remain indeterminate. Focusing on positive extensions—fully defined cooperative games that agree with the partial data and have nonnegative dividends—we introduce a novel, two-stage dividend-assignment procedure that fully characterizes all such extensions. Our method offers a general criterion for positivity-extendability, introduces an explicit lower bound game, and provides an understanding of the structure of extreme points in the extension set. These contributions significantly expand the toolkit for theoretical analyses and practical computations of incomplete cooperative games, and also shed new light on properties of classical cooperative games.
期刊介绍：
Operations Research Letters is committed to the rapid review and fast publication of short articles on all aspects of operations research and analytics. Apart from a limitation to eight journal pages, quality, originality, relevance and clarity are the only criteria for selecting the papers to be published. ORL covers the broad field of optimization, stochastic models and game theory. Specific areas of interest include networks, routing, location, queueing, scheduling, inventory, reliability, and financial engineering. We wish to explore interfaces with other fields such as life sciences and health care, artificial intelligence and machine learning, energy distribution, and computational social sciences and humanities. Our traditional strength is in methodology, including theory, modelling, algorithms and computational studies. We also welcome novel applications and concise literature reviews.
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