Submodularity of some classes of the combinatorial optimization games
- 113 Downloads
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 wordsCombinatorial optimization Game theory Submodularity
Unable to display preview. Download preview PDF.
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.