Geodesic
Necessary conditions of overtaking equilibrium for infinite horizon differential games
Matematičeskaâ teoriâ igr i eë priloženiâ, Tome 5 (2013) no. 2, pp. 105-136

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

This paper is devoted to refining the necessary conditions of Nash equilibrium for infinite horizon games. The right-hand endpoint of the trajectories is free; the search for equilibrium is conducted in the class of open-loop strategies. For adjoint variables of each player, the necessary asymptotic condition of overtaking Nash equilibrium is obtained. For certain cases (in particular, when the 'strictly optimal solution' criterium is employed), it allows to explicitly specify the expression for the adjoint variable. S. M. Aseev, A. V. Kryazhimskii, and V. M. Veliov used such an expression as a necessary condition of optimality for certain infinite horizon control problems. In this paper we also specify an example of linear game with the opposite objective functionals. In this game, there exist multiple Nash equilibria that depend on the choice of the sequence along which the players optimize their actions. These equilibria produce absolutely different results. Also Sorger version of the 'Lanchester-type' differential game is considered.
Keywords: dynamic optimization, differential games, infinite horizon problem, transversality condition for infinity, necessary conditions of equilibrium, overtaking equilibrium, unbounded cost. 
@article{MGTA_2013_5_2_a4,
     author = {Dmitry V. Khlopin},
     title = {Necessary conditions of overtaking equilibrium for infinite horizon differential games},
     journal = {Matemati\v{c}eska\^a teori\^a igr i e\"e prilo\v{z}eni\^a},
     pages = {105--136},
     publisher = {mathdoc},
     volume = {5},
     number = {2},
     year = {2013},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MGTA_2013_5_2_a4/}
}
TY  - JOUR
AU  - Dmitry V. Khlopin
TI  - Necessary conditions of overtaking equilibrium for infinite horizon differential games
JO  - Matematičeskaâ teoriâ igr i eë priloženiâ
PY  - 2013
SP  - 105
EP  - 136
VL  - 5
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/MGTA_2013_5_2_a4/
LA  - ru
ID  - MGTA_2013_5_2_a4
ER  - 
%0 Journal Article
%A Dmitry V. Khlopin
%T Necessary conditions of overtaking equilibrium for infinite horizon differential games
%J Matematičeskaâ teoriâ igr i eë priloženiâ
%D 2013
%P 105-136
%V 5
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/item/MGTA_2013_5_2_a4/
%G ru
%F MGTA_2013_5_2_a4
Dmitry V. Khlopin. Necessary conditions of overtaking equilibrium for infinite horizon differential games. Matematičeskaâ teoriâ igr i eë priloženiâ, Tome 5 (2013) no. 2, pp. 105-136. http://geodesic.mathdoc.fr/item/MGTA_2013_5_2_a4/