Geodesic
Differential game with discrete stopping time
Matematičeskaâ teoriâ igr i eë priloženiâ, Tome 13 (2021) no. 4, pp. 93-128

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

We consider a two agents zero-sum differential game with discrete stopping times. The payoff function may depend both on the stopping time, on the state of the system at this time, and on the player who constitutes this stopping time. To formalize strategies, non-anticipating càdlàg stochastic processes are used. Under the Isaacs condition, the existence of the game value is established. The corresponding near-optimal strategy is constructed with stochastic guide based on an auxiliary model game governed by continuous-time Markov chain.
Keywords: zero-sum two-person games, Dynkin's stopping game, differential games, strategy with guide, near optimal strategies, extremal shift. 
@article{MGTA_2021_13_4_a4,
     author = {Dmitry V. Khlopin},
     title = {Differential game with discrete stopping time},
     journal = {Matemati\v{c}eska\^a teori\^a igr i e\"e prilo\v{z}eni\^a},
     pages = {93--128},
     publisher = {mathdoc},
     volume = {13},
     number = {4},
     year = {2021},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MGTA_2021_13_4_a4/}
}
TY  - JOUR
AU  - Dmitry V. Khlopin
TI  - Differential game with discrete stopping time
JO  - Matematičeskaâ teoriâ igr i eë priloženiâ
PY  - 2021
SP  - 93
EP  - 128
VL  - 13
IS  - 4
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/MGTA_2021_13_4_a4/
LA  - ru
ID  - MGTA_2021_13_4_a4
ER  - 
%0 Journal Article
%A Dmitry V. Khlopin
%T Differential game with discrete stopping time
%J Matematičeskaâ teoriâ igr i eë priloženiâ
%D 2021
%P 93-128
%V 13
%N 4
%I mathdoc
%U http://geodesic.mathdoc.fr/item/MGTA_2021_13_4_a4/
%G ru
%F MGTA_2021_13_4_a4
Dmitry V. Khlopin. Differential game with discrete stopping time. Matematičeskaâ teoriâ igr i eë priloženiâ, Tome 13 (2021) no. 4, pp. 93-128. http://geodesic.mathdoc.fr/item/MGTA_2021_13_4_a4/