Strategically supported cooperation in dynamic games with coalition structures.

*(English)*Zbl 1338.91032Summary: The problem of strategic stability of long-range cooperative agreements in dynamic games with coalition structures is investigated. Based on imputation distribution procedures, a general theoretical framework of the differential game with a coalition structure is proposed. A few assumptions about the deviation instant for a coalition are made concerning the behavior of a group of many individuals in certain dynamic environments. From these, the time-consistent cooperative agreement can be strategically supported by \(\varepsilon\)-Nash or strong \(\varepsilon\)-Nash equilibria. While in games in the extensive form with perfect information, it is somewhat surprising that without the assumptions of deviation instant for a coalition, Nash or strong Nash equilibria can be constructed.

##### MSC:

91A23 | Differential games (aspects of game theory) |

91A12 | Cooperative games |

91A06 | \(n\)-person games, \(n>2\) |

##### Keywords:

cooperative game theory; coalition structure; strategic stability; imputation distribution procedure; deviation instant; \(\varepsilon\)-Nash equilibrium; strong \(\varepsilon\)-Nash equilibrium
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\textit{L. Wang} et al., Sci. China, Math. 59, No. 5, 1015--1028 (2016; Zbl 1338.91032)

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##### References:

[1] | Albizur, M; Zarzuelo, J, On coalitional semivalues, Games Econom Behaviour, 2, 221-243, (2004) · Zbl 1117.91307 |

[2] | Bloch, F, Sequantal formation of coalitions with externalities and fixed payoff division, Games Econom Behaviour, 14, 90-123, (1996) · Zbl 0862.90143 |

[3] | Chen, B; Li, S S; Zhang, Y Z, Strong stability of Nash equilibria in load balancing games, Sci China Math, 57, 1361-1374, (2014) · Zbl 1307.91012 |

[4] | Dockner E, Jorgensen S, Van Long N, et al. Differential Games in Economics and Management Science. Cambridge: Cambridge University Press, 2000 · Zbl 0996.91001 |

[5] | Fudenberg D, Tirole J. Game Theory. Cambridge: HIT Press, 1991 · Zbl 0596.90015 |

[6] | Gao H W, Petrosyan L. Dynamic Cooperative Game (in Chinese). Beijing: Science Press, 2009 |

[7] | Gao, H W; Petrosyan, L; Qiao, H; etal., Transformation of characteristic function in dynamic games, J Syst Sci Inf, 1, 22-37, (2013) |

[8] | Gao, H W; Petrosyan, L; Sedakov, A, Strongly time-consistent solutions for two-stage network games, Procedia Comput Sci, 31, 255-264, (2014) |

[9] | Gao, H W; Qiao, H; Sedakov, A; etal., A dynamic formation procedure of information flow networks, J Syst Sci Inf, 3, 1-14, (2015) |

[10] | Gao, H W; Yang, H J; Wang, G X; etal., The existence theorem of absolute equilibrium about games on connected graph with state payoff vector, Sci China Math, 53, 1483-1490, (2010) · Zbl 1193.91028 |

[11] | Grauer, L V; Petrosyan, L, Multistage games, J Appl Math Mech, 68, 597-605, (2004) · Zbl 1135.91308 |

[12] | Igarashi, A; Yamamoto, Y, Computational complexity of a solution for directed graph cooperative games, J Oper Res Soc China, 1, 405-413, (2013) · Zbl 1276.05075 |

[13] | Kozlovskaya, N; Petrosyan, L; Zenkevich, N, Coalitional solution of a gema-theoretic emission reduction model, Int Game Theory Rev, 12, 275-286, (2010) · Zbl 1209.91125 |

[14] | Kuhn, H W; Kuhn, H W (ed.); Tucker, A W (ed.), Extensive games and the problem of imputation, 193-216, (1953), Princeton · Zbl 0050.14303 |

[15] | Osborne M J, Rubinstein A. A Course in Game Theory. Cambridge: HIT Press, 1996 · Zbl 1194.91003 |

[16] | Owen G. Values of games with a priory unions. In: Henn R, Moeschlin O, eds. Berlin: Mathematical Economy and Game Theory, 1997, 78-88 |

[17] | Parilina, E; Zaccour, G, Node-consistent core for games played over event trees, Automatica, 53, 304-311, (2015) · Zbl 1371.93218 |

[18] | Petrosyan, L, Stable solutions of differential games with several participants (in Russian), Vestnik Leningrad Univ Mat Mekh Astronom, 19, 46-52, (1977) |

[19] | Petrosyan L. Differential Games of Pursuit. Singapore: World Scientific, 1993 · Zbl 0799.90144 |

[20] | Petrosyan, L, Agreeable solutions in differential games, Int J Math Game Theory Algebra, 7, 165-177, (1997) · Zbl 0905.90194 |

[21] | Petrosyan, L; Danilov, N N, Stability of solutions in nonzero sum differential games with transferable payoffs (in Russian), J Leningrad Univ, 1, 52-59, (1979) · Zbl 0419.90095 |

[22] | Petrosyan L, Danilov N N. Cooperative Differential Games and Their Applications (in Russian). Tomsk: Tomsk University Press, 1982 |

[23] | Petrosyan, L; Danilov, N N, Classification of dynamically stable solutions in cooperative differential games (in Russian), Isvestia High School, 7, 24-35, (1986) · Zbl 0645.90107 |

[24] | Petrosyan, L; Mamkina, S, Dynamic games with coalitional structures, Int Game Theory Rev, 8, 295-307, (2006) · Zbl 1184.91033 |

[25] | Petrosyan, L; Zaccour, G, Time-consistent Shapley value of pollution cost reduction, J Econom Dynam Control, 27, 381-398, (2003) · Zbl 1027.91005 |

[26] | Petrosyan L, Zenkevich N A. Game Theory. Singapore: World Scientific, 1996 · Zbl 0863.90145 |

[27] | Petrosyan, L; Zenkevich, N A, Conditions for sustainable cooperation, Contrib Game Theory Manag, 2, 344-355, (2009) · Zbl 1184.91050 |

[28] | Von Neumann J, Morgenstern O. Theory of Games and Economic Behavior. Princeton: Princeton University Press, 1944 · Zbl 0063.05930 |

[29] | Yeung, D W K, An irrational-behavior-proofness condition in cooperative differential games, Int Game Theory Rev, 8, 739-744, (2006) · Zbl 1274.91075 |

[30] | Yeung, D W K; Petrosyan, L, Subgame consistent cooperative solution for NTU dynamic games via variable weights, Automatica, 59, 84-89, (2015) · Zbl 1326.93010 |

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