Non-Zero Sum Network Games with Pairwise Interactions

Authors

  • Mariia A. Bulgakova St. Petersburg State University, 7/9 Universitetskaya nab., Saint Petersburg, 199034, Russia

DOI:

https://doi.org/10.21638/11701/spbu31.2021.03

Abstract

In the paper non-zero sum games on networks with pairwise interactions are investigated. The first stage is network formation stage, where players chose their preferable set of neighbours. In all following stages simultaneous non-zero sum game appears between connected players in network. As cooperative solutions the Shapley value and τ-value are considered. Due to a construction of characteristic function both formulas are simplified. It is proved, that the coeffcient λ in τ-value is independent from network form and number of players or neighbours and is equal to 1/2 . Also it is proved that in this type of games on complete network the Shapley value and τ-value are coincide.

Keywords:

cooperative games, network games, dynamic games, the Shapley value, τ-value

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References

Tijs, S. H. (1987). An axiomatization of the τ-value. Mathematical Social Sciences, 13, 177–181

Dyer, M. and V. Mohanaraj (2011). Pairwise-Interaction Games. ICALP: Automata, Languages and Programming, P. 159–170

Shapley, L. S. (1953). A value for n-person games. Contributions to the theory of games II, ed. by H. W. Kuhn, A. W. Tucker. Princeton. P. 307–317

Bulgakova, M. A. and L. A. Petrosyan (2015). Cooperative network games with pairwise interactions. Mathematical game theory and applications, 4(7), 7–18

Bulgakova, M. A. (2019a) Solutions of network games with pairwise interactions. Vestnik of Saint-Petersburg State university. Series 10. Applied mathematics. Informatics. Control processes, 15(1), 147–156

Bulgakova, M. A. (2019b). About one multistage non-zero sum game on the network. Vestnik of Saint-Petersburg State university. Series 10. Applied mathematics. Informatics. Control processes, 15(4), 603–615

Petrosyan, L. A. and N. N. Danilov (1979). Stability of solutions of non-zero-sum game with transferable payoffs. Vestnik of the Leningrad University. Series 1. Mathematics. Mechanicks. Astronomy, 1, 52–59

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Published

2021-10-30

How to Cite

Bulgakova, M. A. (2021). Non-Zero Sum Network Games with Pairwise Interactions. Contributions to Game Theory and Management, 14, 38–48. https://doi.org/10.21638/11701/spbu31.2021.03

Issue

Vol. 14 (2021)

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.