Template-Type:  ReDIF-Paper 1.0
Series:  Tinbergen Institute Discussion Papers
Creation-Date: 03/15/2019
Number: 19-022/II
Author-Name: Wenna Wang
Author-Workplace-Name: Northwestern Polytechnical University, VU University
Author-Name: Rene van den Brink
Author-Workplace-Name: VU University
Author-Name: Hao Sun
Author-Workplace-Name: Northwestern Polytechnical University
Author-Name: Genjiu Xu
Author-Workplace-Name: Northwestern Polytechnical University
Author-Name: Zhengxing Zou
Author-Workplace-Name: Beijing Institute of Technology, VU University, Amsterdam
Title: The alpha-constant-sum games
Abstract: Given any alpha in [0,1], an alpha-constant-sum game on a finite set of players, N, is a function that assigns a real number to any coalition S (being a subset of the player set N), such that the sum of the worth of the coalition S and the worth of its complementary coalition N\S is alpha times of the worth of the grand coalition N. This class contains the constant-sum games of Khmelnitskaya (2003) (for alpha = 1) and games of threats of Kohlberg and Neyman (2018) (for alpha = 0) as special cases. An alpha-constant-sum game may not be a classical TU cooperative game as it may fail to satisfy the condition that the worth of the empty set is 0, except when alpha = 1.  In this paper, we will build a value theory for the class of alpha-constant-sum games, and mainly introduce the alpha-quasi-Shapley value.  We characterize this value by classical axiomatizations for TU games. We show that axiomatizations of the equal division value do not work on these classes of alpha-constant-sum games. 
Classification-JEL: C71
Keywords: alpha-constant-sum game, alpha-quasi-Shapley value, threat game, constant-sum-game
File-Url: https://papers.tinbergen.nl/19022.pdf
File-Format:  application/pdf
File-Size: 396364 bytes
Handle:  RePEc:tin:wpaper:20190022