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Mathematical Methods of Operations Research

, Volume 58, Issue 1, pp 131–139 | Cite as

Submodularity of some classes of the combinatorial optimization games

  • Yoshio OkamotoEmail author
Article

Abstract.

Submodularity (or concavity) is considered as an important property in the field of cooperative game theory. In this article, we characterize submodular minimum coloring games and submodular minimum vertex cover games. These characterizations immediately show that it can be decided in polynomial time that the minimum coloring game or the minimum vertex cover game on a given graph is submodular or not. Related to these results, the Shapley values are also investigated.

Key words

Combinatorial optimization Game theory Submodularity 

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Notes

Acknowledgments.

The author acknowledges the support by the Berlin-Zürich Joint Graduate Program “Combinatorics, Geometry, and Computation” (CGC). The author is also grateful to Kenji Kashiwabara, Akiyoshi Shioura and Masahiro Hachimori for their valuable comments.

Copyright information

© Springer-Verlag 2003

Authors and Affiliations

  1. 1.Department of Computer ScienceInstitute of Theoretical Computer ScienceZürichSwitzerland

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