Strongly subgame consistent core in stochastic games

Elena M. Parilina ; Leon A. Petrosyan

Matematičeskaâ teoriâ igr i eë priloženiâ, Tome 9 (2017) no. 2, pp. 39-61.

Résumé

Stochastic games defined on finite tree graphs are investigated in the paper. Each node of the graph is defined by a given $n$-person normal form game. Transition to the next vertex of the tree is random and depends on the strategy profile realised in the current game. To determine cooperative solution of the game, the problem of maximization of players' joint total expected payoff is solved. The core is considered as the solution of the cooperative game. The definition of the strong subgame consistency (strong dynamic consistency) of the core is introduced. Method for constructing a cooperative distribution procedure of the imputation from the core which provides strong subgame consistency of the imputation is proposed.

Détail

Keywords: stochastic game, strong subgame consistency, strong time consistency
Mots-clés : core.

Bibliographie

[1] Gromova E. V., Petrosyan L. A., “Silno dinamicheski ustoichivoe kooperativnoe reshenie v odnoi differentsialnoi igre upravleniya vrednymi vybrosami”, Upravlenie bolshimi sistemami, 55 (2015), 140–159

[2] Parilina E. M., “Ustoichivaya kooperatsiya v stokhasticheskikh igrakh”, Matematicheskaya teoriya igr i ee prilozheniya, 2:3 (2010), 21–40

[3] Petrosyan L. A., “Ustoichivost reshenii v differentsialnykh igrakh so mnogimi uchastnikami”, Vestnik Leningradskogo universiteta. Seriya 1: matematika, mekhanika, astronomiya, 1977, no. 19, 46–52

[4] Petrosyan L. A., “Postroenie silno-dinamicheski ustoichivykh reshenii v kooperativnykh differentsialnykh igrakh”, Vestnik Leningradskogo universiteta. Seriya 1: matematika, mekhanika, astronomiya, 1992, no. 2, 33–38

[5] Petrosyan L. A., “Silno dinamicheski ustoichivye printsipy optimalnosti v mnogokriterialnykh zadachakh optimalnogo upravleniya”, Tekhnicheskaya kibernetika, 1993, no. 1, 169–174

[6] Petrosyan L. A., Baranova E. M., Shevkoplyas E. V., “Mnogoshagovye kooperativnye igry so sluchainoi prodolzhitelnostyu”, Optimalnoe upravlenie i differentsialnye igry, Trudy instituta matematiki i mekhaniki, 10, no. 2, 2004, 116–130 | Zbl

[7] Petrosyan L. A., Danilov N. A., “Ustoichivye resheniya neantagonisticheskikh differentsialnykh igr s tranzitivnymi vyigryshami”, Vestnik LGU, 1979, no. 1, 46–54

[8] Petrosyan L. A., Kuzyutin D. V., Igry v razvernutoi forme: optimalnost i ustoichivost, Izd-vo S.-Peterburgskogo universiteta, SPb., 2000

[9] Petrosyan L. A., Zenkevich N. A., “Printsipy ustoichivoi kooperatsii”, Matematicheskaya teoriya igr i ee prilozheniya, 1:1 (2009), 106–123

[10] Petrosyan O. L., Gromova E. V., Pogozhev S. V., “O silno dinamicheski ustoichivom podmnozhestve $C$-yadra v kooperativnykh differentsialnykh igrakh s predpisannoi prodolzhitelnostyu”, Matematicheskaya teoriya igr i ee prilozheniya, 8:4 (2016), 79–106 | Zbl

[11] Pecherskii S. L., Yanovskaya E. B., Kooperativnye igry: resheniya i aksiomy, Izd-vo Evropeiskogo universiteta v S.-Peterburge, SPb., 2004

[12] Sedakov A. A., “O silnoi dinamicheskoi ustoichivosti $c$-yadra”, Matematicheskaya teoriya igr i ee prilozheniya, 7:2 (2015), 69–84 | Zbl

[13] Tur A. V., “Lineino-kvadratichnye stokhasticheskie diskretnye igry so sluchainoi prodolzhitelnostyu”, Matematicheskaya teoriya igr i ee prilozheniya, 6:3 (2014), 76–92 | Zbl

[14] Gillies D. B., “Solutions to general non-zero-sum games”: Tucker A. W., Luce R. D. (eds.), Contributions to the Theory of Games IV, Annals of Mathematics Studies, 40, Princeton University Press, Princeton, 1959, 47–85 | MR

[15] Parilina E., Zaccour G., “Node-Consistent Core for Games Played over Event Trees”, Automatica, 53 (2015), 304–311 | DOI | MR

[16] Petrosjan L. A., “Cooperative Stochastic Games”, Advances in Dynamic Games. Application to Economics, Engineering and Environmental Management, Annals of the ISDG, eds. A. Haurie, S. Muto, L. A. Petrosjan, T. E. S. Raghavan, 2006, 139–146 | MR

[17] Shapley L. S., “Stochastic Games”, Proceedings of National Academy of Sciences of the USA, 39 (1953), 1095–1100 | DOI | MR | Zbl

[18] http://mmiras.webs.uvigo.es/TUGlab/