We study a kind of partial information non-zero sum differential games of mean-field backward doubly stochastic differential equations,in which the coefficient contains not only the state process but also its marginal...We study a kind of partial information non-zero sum differential games of mean-field backward doubly stochastic differential equations,in which the coefficient contains not only the state process but also its marginal distribution,and the cost functional is also of mean-field type.It is required that the control is adapted to a sub-filtration of the filtration generated by the underlying Brownian motions.We establish a necessary condition in the form of maximum principle and a verification theorem,which is a sufficient condition for Nash equilibrium point.We use the theoretical results to deal with a partial information linear-quadratic(LQ)game,and obtain the unique Nash equilibrium point for our LQ game problem by virtue of the unique solvability of mean-field forward-backward doubly stochastic differential equation.展开更多
基金supported in part by the National Natural Science Foundation of China(Grant Nos.11871309,11671229,71871129,11371226,11301298)the National Key R&D Program of China(Grant No.2018 YFA0703900)+2 种基金the Natural Science Foundation of Shandong Province(No.ZR2019MA013)the Special Funds of Taishan Scholar Project(No.tsqn20161041)the Fostering Project of Dominant Discipline and Talent Team of Shandong Province Higher Education Institutions.
文摘We study a kind of partial information non-zero sum differential games of mean-field backward doubly stochastic differential equations,in which the coefficient contains not only the state process but also its marginal distribution,and the cost functional is also of mean-field type.It is required that the control is adapted to a sub-filtration of the filtration generated by the underlying Brownian motions.We establish a necessary condition in the form of maximum principle and a verification theorem,which is a sufficient condition for Nash equilibrium point.We use the theoretical results to deal with a partial information linear-quadratic(LQ)game,and obtain the unique Nash equilibrium point for our LQ game problem by virtue of the unique solvability of mean-field forward-backward doubly stochastic differential equation.
