A New Allocation Rule for Cooperative Games with Hypergraph Communication Structure

Authors

  • David A. Kosian Saint Petersburg State University
  • Leon A. Petrosyan Saint Petersburg State University

Abstract

A new allocation rule was proposed by splitting the original game into a game between hyperlinks and games within them. A special case of cooperative game on flower type hypergraphs is investigated. The proposed allocation rule has been generalized for games with a communication struc¬ture represented by acyclic reduced hypergraphs and was illustrated by examples.

Keywords:

cooperation, characteristic function, hypergraph, communication structure, allocation rule

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References

Myerson R.B. (1977). Graphs and cooperation in games. Math. Oper. Res., 2, 225–229.

Shapley, L.S. (1953). A value for n-person games. Annals of Math. Studies, 28, 307–317.

Owen, G. (1986). Values of graph-restricted games. SIAM J. Alg. Disc. Meth. 7, 210–220.

Meessen, R. (1988). Communication games, Master’s thesis. Department of Mathematics. University of Nijmegen, the Netherlands (in Dutch).

Van den Nouweland, A., Borm, P., Tijs, S. (1992). Allocation rules for hypergraph communication situations. Int. J. Game Theory, 20, 255–268.

Shan, E., G. Zhang, X. Shan (2018). The degree value for games with communication structure. Int. J. Game Theory, 47, 857–871.

Von Neumann, J., Morgenstern, O. (1994). Theory of Games and Economic Behavior. Princeton: Princeton University Press.

Berge, C. (1989). Hypergraphs. North-Holland, Mathematical library, pp. 1–3, 155–162.

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Published

2022-03-09

How to Cite

Kosian, D. A., & Petrosyan, L. A. (2022). A New Allocation Rule for Cooperative Games with Hypergraph Communication Structure. Contributions to Game Theory and Management, 12. Retrieved from https://gametheory.spbu.ru/article/view/12918

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Articles