On the Set of Balanced Games

IF 1.4 3区数学 Q2 MATHEMATICS, APPLIED

Mathematics of Operations Research Pub Date : 2024-08-13 DOI:10.1287/moor.2023.0379

Pedro Garcia-Segador, Michel Grabisch, Pedro Miranda

引用次数: 0

Abstract

We study the geometric structure of the set of cooperative transferable utility games having a nonempty core, characterized by Bondareva and Shapley as balanced games. We show that this set is a nonpointed polyhedral cone, and we find the set of its extremal rays and facets. This study is also done for the set of balanced games whose value for the grand coalition is fixed, which yields an affine nonpointed polyhedral cone. Finally, the case of nonnegative balanced games with fixed value for the grand coalition is tackled. This set is a convex polytope, with remarkable properties. We characterize its vertices and facets, study the adjacency structure of vertices, develop an algorithm for generating vertices in a random uniform way, and show that this polytope is combinatorial and its adjacency graph is Hamiltonian. Last, we give a characterization of the set of games having a core reduced to a singleton.Funding: This work was supported by the Spanish Government [Grant PID2021-124933NB-I00].

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论平衡游戏集

我们研究了具有非空核心的合作可转移效用博弈集合的几何结构，邦达列娃和沙普利将其描述为平衡博弈。我们证明了这个集合是一个无尖多面体圆锥，并找到了其极值射线和极值面的集合。我们还对大联盟值固定的平衡博弈集合进行了研究，得出了一个仿射非指向多面体圆锥。最后，我们还研究了大联盟值固定的非负平衡博弈。这个集合是一个凸多面体，具有显著的特性。我们描述了它的顶点和面的特征，研究了顶点的邻接结构，开发了一种以随机均匀方式生成顶点的算法，并证明了这个多面体是组合型的，其邻接图是哈密尔顿图。最后，我们给出了一个游戏集的特征，该游戏集的核心被简化为一个单子：本文由西班牙政府资助[PID2021-124933NB-I00]。

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

Mathematics of Operations Research 管理科学-应用数学

CiteScore

3.40

自引率

5.90%

发文量

178

审稿时长

15.0 months

期刊介绍： Mathematics of Operations Research is an international journal of the Institute for Operations Research and the Management Sciences (INFORMS). The journal invites articles concerned with the mathematical and computational foundations in the areas of continuous, discrete, and stochastic optimization; mathematical programming; dynamic programming; stochastic processes; stochastic models; simulation methodology; control and adaptation; networks; game theory; and decision theory. Also sought are contributions to learning theory and machine learning that have special relevance to decision making, operations research, and management science. The emphasis is on originality, quality, and importance; correctness alone is not sufficient. Significant developments in operations research and management science not having substantial mathematical interest should be directed to other journals such as Management Science or Operations Research.