RT Journal Article
SR 00
A1 Bensoussan, Alain
A1 Frehse, Jens
A1 Grün, Christine
T1 On a system of PDEs associated to a game with a varying number of players
JF Communications in Mathematical Sciences
YR 2015
FD 2015
VO vol. 13
IS n° 3
SP 623
OP 639
K1 Bellman systems
K1 regularity for PDEs
K1 Nash points
K1 stochastic differential games
AB We consider a general Bellman type system of parabolic partial differential equations with a special coupling in the zero order terms. We show the existence of solutions in Lp((0,T);W2,p(O))nW1,p((0,T)×O) by establishing suitable a priori bounds. The system is related to a certain non zero sum stochastic differential game with a maximum of two players. The players control a diffusion in order to minimise a certain cost functional. During the game it is possible that present players may die or a new player may appear. We assume that the death, respectively the birth time of a player is exponentially distributed with intensities that depend on the diffusion and the controls of the players who are alive.
PB International Press
SN 1539-6746
LK https://publications.ut-capitole.fr/id/eprint/18330/
UL http://tse-fr.eu/pub/29333