Strategically Supported Cooperation in Differential Games with Coalition Structures

Authors

  • Lei Wang Teachers College of Qingdao University
  • Li Song Qingdao University
  • Leon Petrosyan Saint Petersburg State University
  • Artem Sedakov Saint Petersburg State University
  • Hongwei Gao Qingdao University

Abstract

The problem of strategic stability of long-range cooperative agreements in di?erential games with coalition structures is investigated. We build a general theoretical framework of the cooperative di?erential game with a coalition structure basing on imputation distribution procedure. The notion of imputation distribution procedure is the basic ingredient in our theory. This notion may be interpreted as an instantaneous payoff of an individual at some moment which prescribes distribution of the total gain among the members of a group and yields the existence of a Nash equilibrium. Moreover, a few assumptions about deviation instant for a coalition are made concerning behavior of a group of many individuals in certain dynamic environments; thus, the time-consistent cooperative agreement can be strategically supported by an ε-Nash equilibrium or a strong ε-Nash equilibrium.

Keywords:

differential game, coalition structure, strategic stability, imputation distribution procedure, deviation instant

Downloads

Download data is not yet available.

References

Dockner, E., Jorgensen, S., Van Long, N. and Sorger, G. (2000). Differential Games in Economics and Management Science. Cambridge University Press, Cambridge.

Gao, H., Petrosyan, L. (2009). Dynamic Cooperative Game. Beijing: Science Press, 391–399 (in Chinese).

Gao, H., Petrosyan, L., Qiao, H., Sedakov, A., Xu, G. (2013). Transformation of Characteristic Function in Dynamic Games. Journal of Systems Science and Information, 1(1), 22–37.

Gao, H., Petrosyan, L., Sedakov, A. (2014). Strongly Time-Consistent Solutions for Two-Stage Network Games. Procedia Computer Science, 31, 255–264.

Kuhn, H. W. (1953). Extensive Games and the Problem of Imputation. In: Contributions to the Theory of Games II (eds. H. W. Kuhn and A.W. Tucker), Princeton, Princeton University Press, pp. 193–216.

Kozlovskaya, N., Petrosyan, L., Zenkevich, N. (2010). Coalitional Solution of a Gema-Theoretic Emission Reduction Model. International Game Theory Review, 12(3), 275–286.

Petrosyan, L. (1977). Stable Solutions of Differential Games with Many Participants. Viestnik of Leningrad University, 19, 46–52.

Petrosyan, L. (1993). Differential Games of Pursuit. World Scientific, Singapore, pp. 270–282.

Petrosyan, L. (1997). Agreeable Solutions in Differential Games. International Journal of Mathematics, Game Theory and Algebra, 7, 165–177.

Petrosyan, L. and Danilov, N. N. (1979). Stability of Solutions in Nonzero Sum Differential Games with Transferable Payoffs. Journal of Leningrad University N1, 52–59 (in Russian).

Petrosyan, L. and Danilov, N. N. (1982). Cooperative Differential Games and Their Applications. Tomsk University Press, Tomsk.

Petrosyan, L. and Danilov, N. N. (1986). Classification of Dynamically Stable Solutions in Cooperative Differential Games. Isvestia of high school, 7, 24–35 (in Russian).

Petrosyan, L. and Grauer, L. V. (2002). Strong Nash Equilibrium in Multistage Games. International Game Theory Review, 4(3), 244–264.

Petrosjan, L. A., Mamkina, S. I. (2006) Dynamic Games with Coalitional Structures. International Game Theory Review, 8(2), 295–307.

Petrosyan, L. and Zaccour, G. (2003). Time-Consistent Shapley Value of Pollution Cost Reduction. Journal of Economic Dynamics and Control, 27, 381–398.

Petrosyan, L. and Zenkevich, N. A. (1996). Game Theory. World Scientific, Singapore.

Petrosyan, L. and Zenkevich, N. A. (2009). Conditions for Sustainable Cooperation. Contributions to Game Theory and Management, SPb, GSOM, Vol.2, 344–355.

von Neumann, J. and Morgenstern, O. (1944). Theory of Games and Economic Behavior. Princeton University Press, Princeton, NJ.

Yeung, D. W. K., Petrosyan, L. (2005). Subgame Consistent Economic Optimization. Springer, New York, NY.

Yeung, D. W. K. (2006). An Irrational-Behavior-Proofness Condition in Cooperative Differential Games. Int. J. of Game Theory Rew, 8(4), 739–744.

Downloads

Published

2022-05-02

How to Cite

Wang, L., Song, L., Petrosyan , L., Sedakov, A., & Gao, H. (2022). Strategically Supported Cooperation in Differential Games with Coalition Structures. Contributions to Game Theory and Management, 8. Retrieved from https://gametheory.spbu.ru/article/view/13469

Issue

Vol. 8 (2015)

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.