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

Bin Liu (), Han Xiao and Qizhi Fang ()
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Bin Liu: School of Mathematical Sciences, Ocean University of China, Qingdao, P. R. China
Han Xiao: School of Mathematical Sciences, Ocean University of China, Qingdao, P. R. China
Qizhi Fang: School of Mathematical Sciences, Ocean University of China, Qingdao, P. R. China

Asia-Pacific Journal of Operational Research (APJOR), 2021, vol. 38, issue 05, 1-9

Abstract: 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.

Keywords: Cooperative game; population monotonic allocation scheme; independent set (search for similar items in EconPapers)
Date: 2021
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DOI: 10.1142/S0217595921400066

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