Principles of Stable Cooperation in Stochastic Games

Authors

  • Elena M. Parilina Saint Petersburg State University

Abstract

The paper considers stochastic games in the class of stationary strategies. The cooperative form of this class of stochastic games is constructed. The cooperative solution is found. Conditions of dynamic stability for stochastic games are obtained. Principles of dynamic stability include three conditions: subgame consistency, strategic stability and irrational behavior proof condition of the cooperative agreement. Also the paper considers the example for which the cooperative agreement is found and the conditions of dynamic stability are checked.

Keywords:

cooperative stochastic game, stationary strategies, time consistency, subgame consistency, payoff distribution procedure, strategic stability, irrational behavior proof condition

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References

Altman,E., El-Azouzi, R. and Jimenez, T. (2003). Slotted Aloha as a stochastic game with partial information. Proceedings of Modeling and Optimization in Mobile, Ad-Hoc and Wireless Networks (WiOpt ’03), Sophia Antipolis, France.

Amir, R. (2003). Stochastic games in economics: The latter-theoretic approach. Stochastic Games and Applications in A. Neyman and S. Sorin (eds.), NATO Science Series C, Mathematical and Physical Sciences, Vol. 570, Chap. 29, 443–453.

Bellman, R. (1957). Dynamic programming. Princeton University Press, Princeton, NJ.

Dutta, P. (1995). A folk theorem for stochastic games. Journal of Economic Theory 66, 1–32.

Grauer, L.V. and Petrosjan, L.A. (2002). Strong Nash Equilibrium in Multistage Games. International Game Theory Review, 4(3), 255–264.

Herings, P.J.-J. and Peeters, R.J.A.P. (2004). Stationary Equlibria in Stochastic Games: Structure, Selection, and Computation. Journal of Economic Theory, Vol. 118, No. 1, 32–60.

Parilina, E.M. (2010). Cooperative data transmission game in wireless network. Upravlenie bol’simi sistemami, 31.1, 93–110 (in Russian).

Petrosyan, L.A. (1977). Stability of the solutions in differential games with several players. Vestnik Leningrad. Univ. Mat. Mekh. Astronom, 19(4), 46–52 (in Russian).

Petrosjan, L.A. (2006). Cooperative Stochastic Games. Advances in dynamic games, Annals of the International Society of Dynamic Games, Vol. 8, Part VI, 139–146.

Petrosjan, L.A. and Baranova, E.M. (2006). Cooperative Stochastic Games in Stationary Strategies. Game Theory and Applications, XI, 7–17.

Petrosjan, L.A. and Danilov, N.N. (1979). Stability of the solutions in nonantagonistic differential games with transferable payoffs. Vestnik Leningrad. Univ. Mat. Mekh. Astronom. 1, 52–59.

Petrosyan, L.A. and Zenkevich, N.A. (2009). Principles of dynamic stability. Upravlenie bol’simi sistemami, 26.1, 100–120 (in Russian).

Petrosyan, L.A., Baranova, E.M., Shevkoplyas, E.V. (2004). Multistage Cooperative Games with Random Duration. Optimal control and differential games. Proceedings of Institute of mathematics and mechanics, 10(2), 116–130 (in Russian).

Raghavan, T.E.S. (2006). A Stochastic Game Model of Tax Evasion. Advances in dynamic games, Annals of the International Society of Dynamic Games, 2006, Vol. 8, Part VI, 397–420.

Shapley, L.S. (1953a). Stochastic Games. Proceedings of National Academy of Sciences of the USA, 39, 1095–1100.

Shapley, L.S. (1953b). A Value for n-person Games. Contributions to the Theory of Games-II, by H.W. Kuhn and A.W. Tucker, editors. (Annals of Mathematical Studies, Vol. 28), Princeton University Press, 307–317.

Yeung, D.W.K. (2006). An irrational-behavior-proof condition in cooperative differential games. International Game Theory Review, 8(4), 739–744.

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Published

2023-01-25

How to Cite

Parilina, E. M. (2023). Principles of Stable Cooperation in Stochastic Games. Contributions to Game Theory and Management, 5, 243–256. Retrieved from https://gametheory.spbu.ru/article/view/14489

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.