Geodesic
Two-level cooperation in a class of non-zero-sum differential games
Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 25 (2019) no. 1, pp. 166-173
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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.
Mots-clés : coalition partition
Keywords: cooperative differential game with transferable payoffs, Pareto optimality, payoff distribution procedure, time consistency. 
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L. A. Petrosyan; D. W. K. Yeung. Two-level cooperation in a class of non-zero-sum differential games. Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 25 (2019) no. 1, pp. 166-173. http://geodesic.mathdoc.fr/item/TIMM_2019_25_1_a12/

[1] Eichengreen B., Irwin D., “Trade blocs, currency blocs, and the reorientation of trade in the 1930s”, J. Internat. Economics, 38 (1995), 1–24 | DOI

[2] McDonald F., Tuselmann J.H., Voronkova S., Golesorkhi S., “The strategic development of subsidiaries in regional trade blocs”, The Multinational Business Review, 19:3 (2011), 256–271 | DOI

[3] Frankel J.A., Rose A., “The endogeneity of the optimum currency area criteria”, Economic J., 108 (1998), 1009–1025 | DOI

[4] Kandogan Y., “Consistent estimates of regional blocs'trade effects”, Review Internat. Economics, 16:2 (2008), 301–314 | DOI

[5] Schott J.J., “Trading blocs and the world trading system”, World Economy, 14:1 (1991), 1–17 | DOI

[6] Wolf N., Ritschl A.O., “Endogeneity of currency areas and trade vlocs: Evidence from a natural experiment”, KYKLOS, 64:2 (2011), 219–312 | DOI

[7] Petrosyan L.A., Yeung D.W.K., “The two level cooperation in a class of n-person differential games”, 17th IFAC Workshop on Control Applications of Optimization CAO 2018 (Yekaterinburg, Russia, 15-19 October 2018), IFAC-PapersOnLine, 51, no. 32, 2018, 585–587 | DOI | MR

[8] Petrosyan L.A., E.V. Gromova, “Dvukhurovnevaya kooperatsiya v koalitsionnykh differentsialnykh igrakh”, Tr. In-ta matematiki i mekhaniki UrO RAN, 20:3 (2014), 193–203 | MR

[9] Yeung D.W.K., Petrosyan L. A., Subgame sonsistent sooperation. A somprehensive treatise, Ser. Theory and Decision Library C, 47, Springer, N Y etc., 2016, 520 pp. | DOI | MR

[10] Petrosyan L. A., Yeung D.W.K., “A Time-consistent solution formula for bargaining problem in differential games”, Internat. Game Theory Review, 16:4 (2014), 1–24 | DOI | MR

[11] Petrosyan L.A., Danilov N.N., “Ustoichivost reshenii neantagonisticheskikh differentsialnykh igr s transferabelnymi vyigryshami”, Vest. Leningrad. un-ta. Ser. 1: Matematika, mekhanika, astronomiya, 1979, no. 1, 52–59 | Zbl

[12] Petrosyan L., Zaccour G., “Time-consistent Shapley value allocation of pollution cost reduction”, J. Economic Dynamics Control, 27:3 (2003), 381–398 | DOI | MR

[13] Yeung D.W.K., Petrosyan L. A., Cooperative stochastic differential games, Springer, N Y etc., 2006, 242 pp. | MR | Zbl