The alpha-constant-sum games

Wenna Wang, Rene van den Brink, Hao Sun, Genjiu Xu and Zhengxing Zou
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Wenna Wang: Northwestern Polytechnical University, VU University
Rene van den Brink: VU University
Hao Sun: Northwestern Polytechnical University
Genjiu Xu: Northwestern Polytechnical University

No 19-022/II, Tinbergen Institute Discussion Papers from Tinbergen Institute

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.

Keywords: alpha-constant-sum game; alpha-quasi-Shapley value; threat game; constant-sum-game (search for similar items in EconPapers)
JEL-codes: C71 (search for similar items in EconPapers)
New Economics Papers: this item is included in nep-gth
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