On a system of PDEs associated to a game with a varying number of players

Bensoussan, Alain, Frehse, Jens and Grün, Christine (2015) On a system of PDEs associated to a game with a varying number of players. Communications in Mathematical Sciences, vol. 13 (n° 3). pp. 623-639.

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Official URL: http://tse-fr.eu/pub/29333


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.

Item Type: Article
Language: English
Date: 2015
Refereed: Yes
Uncontrolled Keywords: Bellman systems, regularity for PDEs, Nash points, stochastic differential games
Divisions: TSE-R (Toulouse)
Site: UT1
Date Deposited: 21 Sep 2015 13:08
Last Modified: 29 Mar 2018 13:09
OAI ID: oai:tse-fr.eu:29333
URI: http://publications.ut-capitole.fr/id/eprint/18330

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