Abstract
This paper investigates the conditions for the existence of open-loop and closed-loop Nash equilibria for the linear quadratic (LQ) two-player stochastic difference game. It is shown that the former is characterized by the solvability of a forward–backward stochastic difference equation (FBSΔE), while the latter is described by the solvability of a class of coupled symmetric difference Riccati equations (ΔREs). Different from the existing works, the relationship between the closed-loop representation of open-loop Nash equilibrium and the closed-loop Nash equilibrium has been studied. It is found that the closed-loop representation of open-loop Nash equilibrium is different from the outcome of closed-loop Nash equilibrium for the general case. However, for the LQ zero-sum stochastic difference game, they are consistent.
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