A Combinatorial Characterization for Population Monotonic Allocations in Convex Independent Set Games

被引：1

作者：

Liu, Bin ^{[1
]}

Xiao, Han ^{[1
]}

Fang, Qizhi ^{[1
]}

机构：

[1] Ocean Univ China, Sch Math Sci, Qingdao, Peoples R China

来源：

ASIA-PACIFIC JOURNAL OF OPERATIONAL RESEARCH | 2021年 / 38卷 / 05期

基金：

中国国家自然科学基金;

关键词：

Cooperative game; population monotonic allocation scheme; independent set;

D O I：

10.1142/S0217595921400066

中图分类号：

C93 [管理学]; O22 [运筹学];

学科分类号：

070105 ; 12 ; 1201 ; 1202 ; 120202 ;

摘要：

Independent set games are cooperative games defined on graphs, where players are edges and the value of a coalition is the maximum size of independent sets in the subgraph defined by the coalition. In this paper, we study population monotonic allocation schemes for independent set games. For independent set games introduced by Deng et al. [X. Deng, T. Ibaraki and H. Nagamochi (1999). Algorithmic aspects of the core of combinatorial optimization games. Mathematics of Operations Research, 24(3), 751-766], we provide a combinatorial characterization for population monotonic allocation schemes in convex instances. For independent set games introduced by Xiao et al. [H. Xiao, Y. Wang and Q. Fang (2021). On the convexity of independent set games. Discrete Applied Mathematics, 291, 271-276], we prove the equivalence of convexity, population monotonicity and balancedness.

引用

页数：9