Geodesic
Public good differential game with composite distribution of random time horizon
Contributions to game theory and management, Tome 16 (2023), pp. 7-19.

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

Differential games with random duration are considered. In some cases, the probability density function of the terminal time can change depending on different conditions and we cannot use the standard distribution. The purpose of this work is studying of games with a composite distribution function for terminal time using the dynamic programming methods. The solutions of the cooperative and non-cooperative public good differential game with random duration are considered.
Keywords: differential games, optimal control, dynamic programming, Hamilton-Jacobi-Bellman equation. 
@article{CGTM_2023_16_a1,
     author = {Tatyana Balas and Anna Tur},
     title = {Public good differential game with composite distribution of random time horizon},
     journal = {Contributions to game theory and management},
     pages = {7--19},
     publisher = {mathdoc},
     volume = {16},
     year = {2023},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/CGTM_2023_16_a1/}
}
TY  - JOUR
AU  - Tatyana Balas
AU  - Anna Tur
TI  - Public good differential game with composite distribution of random time horizon
JO  - Contributions to game theory and management
PY  - 2023
SP  - 7
EP  - 19
VL  - 16
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/CGTM_2023_16_a1/
LA  - en
ID  - CGTM_2023_16_a1
ER  - 
%0 Journal Article
%A Tatyana Balas
%A Anna Tur
%T Public good differential game with composite distribution of random time horizon
%J Contributions to game theory and management
%D 2023
%P 7-19
%V 16
%I mathdoc
%U http://geodesic.mathdoc.fr/item/CGTM_2023_16_a1/
%G en
%F CGTM_2023_16_a1
Tatyana Balas; Anna Tur. Public good differential game with composite distribution of random time horizon. Contributions to game theory and management, Tome 16 (2023), pp. 7-19. http://geodesic.mathdoc.fr/item/CGTM_2023_16_a1/

[1] Balas, T. N., “One hybrid optimal control problem with multiple switches”, Control Process. Stab., 9 (2022), 379–386

[2] Balas, T., Tur, A., “The Hamilton-Jacobi-Bellman Equation for Differential Games with Composite Distribution of Random Time Horizon”, Mathematics, 11:2 (2023), 462 | DOI

[3] Bellman, R., Princeton, NJ, USA, Princeton University Press, 1957

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

[5] Gromov, D., Gromova, E., “Differential games with random duration: A hybrid systems formulation”, Contrib. Game Theory Manag., 7 (2014), 104–119 | MR

[6] Gromov, D., Gromova, E., “On a Class of Hybrid Differential Games”, Dyn. Games Appl., 7 (2017), 266–288 | DOI | MR | Zbl

[7] Kostyunin, S., Shevkoplyas, E., “On simplification of integral payoff in the differential games with random duration”, Vestn. St. Petersburg Univ. Math., 4 (2011), 47–56

[8] Petrosyan, L. A., Shevkoplyas, E. V., “Cooperative Solution for Games with Random Duration”, Game Theory Appl., 9 (2003), 125–139 | MR

[9] Shevkoplyas, E. V., “The Hamilton-Jacobi-Bellman equation for a class of differential games with random duration”, Math. Game Theory Appl., 1 (2009), 98–118 | Zbl

[10] Shevkoplyas, E., Kostyunin, S., “Modeling of Environmental Projects under Condition of a Random Time Horizon”, Contrib. Game Theory Manag., 4 (2011), 447–459 | MR | Zbl

[11] Yaari, M. E., “Uncertain Lifetime, Life Insurance, and the Theory of the Consumer”, Rev. Econ. Stud., 32 (1965), 137–150 | DOI