A generalization of the Shapley-Ichiishi result

被引:8
|
作者
Kuipers, Jeroen [1 ]
Vermeulen, Dries [2 ]
Voorneveld, Mark [3 ]
机构
[1] Maastricht Univ, Dept Knowledge Engn, NL-6200 MD Maastricht, Netherlands
[2] Maastricht Univ, Dept Quantitat Econ, NL-6200 MD Maastricht, Netherlands
[3] Stockholm Sch Econ, Dept Econ, S-11383 Stockholm, Sweden
关键词
TU games; Core; Linearity regions; Computation of Q-sets; TALMUD; GAMES;
D O I
10.1007/s00182-010-0239-5
中图分类号
F [经济];
学科分类号
02 ;
摘要
The Shapley-Ichiishi result states that a game is convex if and only if the convex hull of marginal vectors equals the core. In this paper, we generalize this result by distinguishing equivalence classes of balanced games that share the same core structure. We then associate a system of linear inequalities with each equivalence class, and we show that the system defines the class. Application of this general theorem to the class of convex games yields an alternative proof of the Shapley-Ichiishi result. Other applications range from computation of stable sets in non-cooperative game theory to determination of classes of TU games on which the core correspondence is additive (even linear). For the case of convex games we prove that the theorem provides the minimal defining system of linear inequalities. An example shows that this is not necessarily true for other equivalence classes of balanced games.
引用
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页码:585 / 602
页数:18
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