Positivity of incomplete cooperative games revisited

IF 0.8 4区管理学 Q4 OPERATIONS RESEARCH & MANAGEMENT SCIENCE

Operations Research Letters Pub Date : 2025-03-12 DOI:10.1016/j.orl.2025.107277

Martin Černý

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.

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我们考虑不完全合作博弈，其中只有一些联盟的值是指定的，其他联盟的值是不确定的。专注于正可拓——完全定义的合作博弈，与部分数据一致且具有非负红利——我们引入了一种新的、两阶段的红利分配过程，它充分表征了所有这些可拓。我们的方法提供了正可扩展性的一般准则，引入了显式下界对策，并提供了对可拓集中极值点结构的理解。这些贡献极大地扩展了不完全合作对策的理论分析和实际计算工具，并对经典合作对策的性质有了新的认识。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Operations Research Letters 管理科学-运筹学与管理科学

CiteScore

2.10

自引率

9.10%

发文量

111

审稿时长

83 days

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.