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This paper is concerned with recursive nonzero-sum stochastic differential game problem in Markovian framework when the drift of the state process is no longer bounded but only satisfies the linear growth condition. The costs of players are given by the initial values of related backward stochastic differential equations which, in our case, are multidimensional with continuous coefficients, whose generators are of linear growth on the volatility processes and stochastic monotonic on the value processes. We finally show the well-posedness of the costs and the existence of a Nash equilibrium point for the game under the generalized Isaacs assumption.

This paper is concerned with a dynamic game of *N* weakly-coupled linear backward stochastic differential equation (BSDE) systems involving mean-field interactions. The backward mean-field game (MFG) is introduced to establish the backward decentralized strategies. To this end, we introduce the notations of Hamiltonian-type consistency condition (HCC) and Riccati-type consistency condition (RCC) in BSDE setup. Then, the backward MFG strategies are derived based on HCC and RCC respectively. Under mild conditions, these two MFG solutions are shown to be equivalent. Next, the approximate Nash equilibrium of derived MFG strategies are also proved. In addition, the scalar-valued case of backward MFG is solved explicitly. As an illustration, one example from quadratic hedging with relative performance is further studied.

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