Geodesic
Coalition Formation in Dynamic Multicriteria Games
Matematičeskaâ teoriâ igr i eë priloženiâ, Tome 10 (2018) no. 2, pp. 40-61 Cet article a éte moissonné depuis la source Math-Net.Ru

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In this paper, new approaches to obtain optimal behavior in dynamic multicriteria games are suggested. The multicriteria Nash equilibrium is designed via the Nash bargaining scheme (Nash products), and the cooperative equilibrium is determined by the Nash bargaining solution for the entire planning horizon. The process of coalition formation in dynamic mul-ticriteria games is studied. For constructing the characteristic function the Nash bargaining scheme is applied, where the multicriteria Nash equilibrium plays the role of the status quo points. Two modifications of the characteristic function are presented that take into account the information structure of the game (the models without and with information). The dynamic multicriteria bioresource management problem is considered. The players’ strategies and the quantities of resource are compared under the cooperative and noncooperative behavior for the above modifications of the characteristic function.
Keywords: dynamic games, ash equilibrium, cooperative equilibrium, characteristic function, Nash bargaining scheme.
Mots-clés : multicriteria games 
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     author = {Anna N. Rettieva},
     title = {Coalition {Formation} in {Dynamic} {Multicriteria} {Games}},
     journal = {Matemati\v{c}eska\^a teori\^a igr i e\"e prilo\v{z}eni\^a},
     pages = {40--61},
     year = {2018},
     volume = {10},
     number = {2},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MGTA_2018_10_2_a2/}
}
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Anna N. Rettieva. Coalition Formation in Dynamic Multicriteria Games. Matematičeskaâ teoriâ igr i eë priloženiâ, Tome 10 (2018) no. 2, pp. 40-61. http://geodesic.mathdoc.fr/item/MGTA_2018_10_2_a2/

[1] Mazalov V. V., Rettieva A. N., “Fish wars with many players”, International Game Theory Review, 12:4 (2010), 385–405 | DOI | MR | Zbl

[2] Patrone F., Pusillo L., Tijs S. H., “Multicriteria games and potentials”, Top, 15 (2007), 138–145 | DOI | MR | Zbl

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

[4] Pieri G., Pusillo L., “Multicriteria Partial Cooperative Games”, Applied Mathematics, 6:12 (2015), 2125–2131 | DOI

[5] Pusillo L., Tijs S., “E-equilibria for multicriteria games”, Annals of ISDG, 12 (2013), 217–228 | MR

[6] Rettieva A. N., “Multicriteria dynamic games”, International Game Theory Review, 1:19 (2017), 1750002 | DOI | MR | Zbl

[7] Rettieva A. N., “A discrete-time bioresource management problem with asymmetric players”, Automation and Remote Control, 75:9 (2014), 1665–1676 | DOI

[8] Shapley L. S., “Equilibrium points in games with vector payoffs”, Naval Research Logistic Quarterly, 6 (1959), 57–61 | DOI | MR

[9] Voorneveld M., Grahn S., Dufwenberg M., “Ideal equilibria in noncooperative multicriteria games”, Mathematical Methods of Operations Research, 52 (2000), 65–77 | DOI | MR | Zbl