Spectrum value for coalitional games

• 成果类型: Article
• 署名作者: Alvarez-Mozos, Mikel; Hellman, Ziv; Winter, Eyal
• 署名单位: Universidade de Santiago de Compostela; Tel Aviv University; Hebrew University of Jerusalem; Hebrew University of Jerusalem; University of Leicester
• 刊物名称: GAMES AND ECONOMIC BEHAVIOR
• ISSN/ISSBN: 0899-8256
• DOI: 10.1016/j.geb.2013.06.011
• 发表日期: 2013
• 页码: 132-142
• 关键词: Coalitional games; Shapley value; Restricted cooperation; Political spectrum

摘要

Assuming a 'spectrum' or ordering of the players of a coalitional game, as in a political spectrum in a parliamentary situation, we consider a variation of the Shapley value in which coalitions may only be formed if they are connected with respect to the spectrum. This results in a naturally asymmetric power index in which positioning along the spectrum is critical. We present both a characterization of this value by means of properties and combinatoric formulae for calculating it. In simple majority games, the greatest power accrues to 'moderate' players who are located neither at the extremes of the spectrum nor in its center. In supermajority games, power increasingly accrues towards the extremes, and in unanimity games all power is held by the players at the extreme of the spectrum. (C) 2013 Elsevier Inc. All rights reserved.