On a class of vertices of the core

• 成果类型: Article
• 署名作者: Grabisch, Michel; Sudholter, Peter
• 署名单位: Paris School of Economics; heSam Universite; Universite Pantheon-Sorbonne; University of Southern Denmark; University of Southern Denmark
• 刊物名称: GAMES AND ECONOMIC BEHAVIOR
• ISSN/ISSBN: 0899-8256
• DOI: 10.1016/j.geb.2017.09.001
• 发表日期: 2018
• 页码: 541-557
• 关键词: TU games; Restricted cooperation; Game with precedence constraints; core; Vertex

摘要

It is known that for supermodular TU-games, the vertices of the core are the marginal vectors, and this result remains true for games where the set of feasible coalitions is a distributive lattice. Such games are induced by a hierarchy (partial order) on players. We propose a larger class of vertices for games on distributive lattices, called min-max vertices, obtained by minimizing or maximizing in a given order the coordinates of a core element. We give a simple formula which does not need to solve an optimization problem to compute these vertices, valid for connected hierarchies and for the general case under some restrictions. We find under which conditions two different orders induce the same vertex for every game, and show that there exist balanced games whose core has vertices which are not min-max vertices if and only if n > 4. (C) 2017 Elsevier Inc. All rights reserved.