Stochastic Differential Games with a Varying Number of Players



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American Institute of Mathematical Sciences


We consider a non zero sum stochastic differential game with a maximum n players, where the players control a diffusion in order to minimisena certain cost functional. During the game it is possible that present players may die or new players may appear. 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. We show how the game is related to a system of partial differential equations with a special coupling in the zero order terms. We provide an existence result for solutions in appropriate spaces that allow to construct Nash optimal feedback controls. The paper is related to a previous result in a similar setting for two players leading to a parabolic system of Bellman equations [4]. Here, we study the elliptic case (infinite horizon) and present the generalisation to more than two players.



Stochastic differential games, Differential equations, Partial, Bellman equations

US National Science Foundation (DMS-1303775); NR-10-BLAN 0012; Research Grants Council of HKSAR (CityU 500113).


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