Generalized Proportional Solutions to Games with Restricted Cooperation

Authors

  • Natalia I. Naumova Saint Petersburg State University

Abstract

In TU-cooperative game with restricted cooperation the values of characteristic function v(S) are defined only for S∈A,where A is a collection of some nonempty coalitions of players. If A is a set of all singletones, then a claim problem arises, thus we have a claim problem with coalition demands. We examine several generalizations of the Proportional method for claim problems: the Proportional solution, the Weakly Proportional solution, the Proportional Nucleolus, and g-solutions that generalize the Weighted Entropy solution. We describe necessary and sufficient condition on A for inclusion the Proportional Nucleolus in the Weakly Proportional solution and necessary and sufficient condition on A for inclusion g-solution in the Weakly Proportional solution. The necessary and sufficient condition on A for coincidence g-solution and the Weakly Proportional solution and sufficient condition for coincidence all g-solutions and the Proportional Nucleolus are obtained.

Keywords:

claim problem, cooperative games, proportional solution, weighted entropy, nucleolus

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References

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Published

2023-01-25

How to Cite

Naumova, N. I. (2023). Generalized Proportional Solutions to Games with Restricted Cooperation. Contributions to Game Theory and Management, 5, 230–242. Retrieved from https://gametheory.spbu.ru/article/view/14488

Issue

Vol. 5 (2012)

Section

Articles

License

Articles of "Contributions to Game Theory and Management" are open access distributed under the terms of the License Agreement with Saint Petersburg State University, which permits to the authors unrestricted distribution and self-archiving free of charge.