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 .
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