Geodesic
On the Construction of the Characteristic Function in Cooperative Differential Games with Random Duration
Contributions to game theory and management, Tome 1 (2007), pp. 460-477.

Voir la notice de l'article provenant de la source Math-Net.Ru

The class of cooperative differential games with random duration is studied. The problem of characteristic function construction is researched. The Hamilton–Jacobi–Bellman equation for the problem with random duration is derived. The method of calculating the characteristic function values with the help of given equation is represented as algorithm. The results are illustrated with the examples.
Keywords: Cooperation, differential games, random duration, characteristic function, the Hamilton–Jacobi–Bellman equation, resource extraction. 
@article{CGTM_2007_1_a27,
     author = {Ekaterina Shevkoplyas},
     title = {On the {Construction} of the {Characteristic} {Function} in {Cooperative} {Differential} {Games} with {Random} {Duration}},
     journal = {Contributions to game theory and management},
     pages = {460--477},
     publisher = {mathdoc},
     volume = {1},
     year = {2007},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/CGTM_2007_1_a27/}
}
TY  - JOUR
AU  - Ekaterina Shevkoplyas
TI  - On the Construction of the Characteristic Function in Cooperative Differential Games with Random Duration
JO  - Contributions to game theory and management
PY  - 2007
SP  - 460
EP  - 477
VL  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/CGTM_2007_1_a27/
LA  - en
ID  - CGTM_2007_1_a27
ER  - 
%0 Journal Article
%A Ekaterina Shevkoplyas
%T On the Construction of the Characteristic Function in Cooperative Differential Games with Random Duration
%J Contributions to game theory and management
%D 2007
%P 460-477
%V 1
%I mathdoc
%U http://geodesic.mathdoc.fr/item/CGTM_2007_1_a27/
%G en
%F CGTM_2007_1_a27
Ekaterina Shevkoplyas. On the Construction of the Characteristic Function in Cooperative Differential Games with Random Duration. Contributions to game theory and management, Tome 1 (2007), pp. 460-477. http://geodesic.mathdoc.fr/item/CGTM_2007_1_a27/

[1] Dockner E., Jorgensen S., van Long N., Sorger G., Differential Games in Economics and Management Science, Cambridge University Press, 2000 | MR | Zbl

[2] Petrosjan L. A., Zaccour G., “Time-consistent Shapley Value Allocation of Pollution Cost Reduction”, Journal of Economic Dynamics and Control, 27 (2003), 381–398 | DOI | MR | Zbl

[3] Petrosjan L. A., Shevkoplyas E. V., “Cooperative Solutions for Games with Random Duration”, Game Theory and Applications, IX, Nova Science Publishers, 2003, 125–139 | MR

[4] Bellman R., Dynamic programming, Princeton University Press, Princeton, NJ, 1957 | MR | Zbl

[5] Shevkoplyas E. V., “The Hamilton–Jacobi–Bellman equation for cooperative differential games with random duration”, Stability and Control Processes Conference, Ext. abstracts (St. Petersburg, 2005), 2005, 630–639 (in Russian)

[6] Shevkoplyas E. V., “On the Construction of the Characteristic Function in Cooperative Differential Games with Random Duration”, Control Theory and Theory of Generalized Solutions of Hamilton–Jacobi Equations, International Seminar CGS'2005, Ext. abstracts (Ekaterinburg, Russia, 2005), v. 1, 2005, 262–270 (in Russian)

[7] Petrosjan L. A., Murzov N. V., “Game Theoretic Model in Mechanics”, Litovskyi matematicheskyi sbornik, VI (1966), 423–432 | MR

[8] Pontryagin L. S., Boltyansky V. G., Mathematical Theory of Optimal Processes, Nauka, M., 1976 | Zbl

[9] Vorobyev N. N., Game Theory for Economists and Cybernetics, Nauka, M., 1985 | MR