Abstract
This article studies a linear quadratic non-zero sum stochastic differential game with overlapping information, where the state dynamics are described by a backward stochastic differential equation and the information obtained by two players has a common part but no inclusion relation. The open-loop Nash equilibrium strategy is given by some conditional mean-field stochastic differential equations. In addition, coupled Riccati equations are introduced to express the state feedback form of the Nash equilibrium strategy.
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