L.A. Petrosyan, D.W.K. Yeung. Two-level cooperation in a class of non-zero-sum differential games ... P. 166-173

Vol. 25, no. 1, 2019

A two-level game is considered. At the first level, the set of players $N$ is partitioned into coalitions $S_i\subset N$, $i=1,\ldots,m$, such that $S_i\cap S_j=\varnothing$ for $i\neq j$ and each coalition plays against other coalitions a non-zero-sum cooperative differential game with prescribed duration and nontransferable payoffs. At the second level, within each coalition, the players are engaged in a cooperative differential game with prescribed duration and transferrable payoffs. The concept of solution is proposed for this type of two-level games. The properties of a solution, namely, its time consistency or dynamic stability, are studied.

Keywords: coalition partition, cooperative differential game with transferable payoffs, Pareto optimality, payoff distribution procedure, time consistency

Received December 12, 2018

Revised December 27, 2018

Accepted January 14, 2019

Funding Agency: This work was supported by the Russian Science Foundation (project no. 17-11-01079).

Leon Aganesovich Petrosyan, Dr. Phys.-Math. Sci., Prof., Saint Petersburg State University, St. Petersburg, 199034 Russia, e-mail: l.petrosyan@spbu.ru.

David W.K. Yeung, Prof. Dr. Dr.h.c., Hong Kong Shue Yan University, Hong Kong, China, e-mail: dwkyeung@hksyu.edu

Cite this article as:   L.A. Petrosyan, D.W.K. Yeung. Two-level cooperation in a class of non-zero-sum differential games, Trudy Instituta Matematiki i Mekhaniki URO RAN, 2019, vol. 25, no. 1, pp. 166–173 . 

REFERENCES

1.   Eichengreen B., Irwin D. Trade blocs, currency blocs, and the reorientation of trade in the 1930s. J. Internat. Economics, 1995, vol. 38, no. 1-2, pp. 1–24. doi: 10.1016/0022-1996(95)92754-P 

2.   McDonald F., Tuselmann J.H., Voronkova S., Golesorkhi S. The strategic development of subsidiaries in regional trade blocs. The Multinational Business Review, 2011, vol. 19, no. 3, pp. 256–271. doi: 10.1108/15253831111172685 

3.   Frankel J.A., Rose A. The endogeneity of the optimum currency area criteria. Economic J., 1998, vol. 108, no. 449, pp. 1009–1025. doi: 10.1111/1468-0297.00327 

4.   Kandogan Y. Consistent estimates of regional blocs’ trade effects. Review Internat. Economics, 2008, vol. 16, no. 2, pp. 301–314. doi: 10.1111/j.1467-9396.2008.00736.x 

5.   Schott J.J. Trading blocs and the world trading system. World Economy, 1991, vol. 14, no. 1, pp. 1–17. doi: 10.1111/j.1467-9701.1991.tb00748.x 

6.   Wolf N., Ritschl A.O. Endogeneity of currency areas and trade blocs: Evidence from a natural experiment. KYKLOS, 2011, vol. 64, no. 2, pp. 219–312. doi: j.1467-6435.2011.00507.x 

7.   Petrosyan L.A. Yeung D.W.K. The two level cooperation in a class of n-person differential games. IFAC-PapersOnLine, 2018, vol. 51, iss. 32, pp. 585–587. doi: 10.1016/j.ifacol.2018.11.486 

8.   Petrosyan L.A., Gromova E.V. Two-level cooperation in coalitional differential games. Trudy Inst. Mat. Mekh. UrO RAN, 2014, vol. 20, no. 3, pp. 193–203.

9.   Yeung D.W.K., Petrosyan L.A. Subgame consistent cooperation. A Comprehensive treatise. Ser. Theory and Decision Library C, vol. 47, N Y etc.: Springer, 2016, 520 p. ISBN: 978-981-10-1545-8 .

10.   Petrosyan L.A., Yeung D.W.K. A time-consistent solution formula for bargaining problem in differential games. Internat. Game Theory Review, 2014, vol. 16, no. 4, pp. 1–24. doi: 10.1142/S0219198914500169 

11.   Petrosyan L.A., Danilov N.N. Stability of solutions in non-antagonistic differential games with transferable payoffs. Vestnik Leningrad. Univ. Math., 1980, vol. 12, pp. 37–45.

12.   Petrosyan L., Zaccour G. Time-consistent Shapley value allocation of pollution cost reduction. J. Economic Dynamics Control, 2003, vol. 27, no. 3, pp. 381–398. doi: 10.1016/S0165-1889(01)00053-7 

13.   Yeung D.W.K., Petrosyan L.A. Cooperative stochastic differential games. N Y etc.: Springer, 2006, 242 р. ISBN: 0387276203 .