标题： 时间不一致的随机线性二次微分博弈 显示英文标题

标题： Time-Inconsistent Stochastic Linear-quadratic Differential Game

摘要： 我们研究了一类一般的时间不一致随机线性二次微分博弈问题。时间不一致性来源于目标泛函中关于期望状态的二次项以及与状态相关的项。我们定义了一种均衡策略，它不同于经典的策略，并通过一组正向-反向随机微分方程推导出均衡策略的充分条件。当状态是一维且系数均为确定性时，我们找到了一个显式的均衡策略。此外，还给出了该均衡策略的唯一性证明。 显示英文摘要

摘要： We consider a general time-inconsistent stochastic linear-quadratic differential game. The time-inconsistency arises from the presence of quadratic terms of the expected state as well as state-dependent term in the objective functionals. We define an equilibrium strategy, which is different from the classical one, and derived a sufficient conditions for equilibrium strategies via a system of forward-backward stochastic differential equations. When the state is one-dimensional and the coefficients are all deterministic, we find an explicit equilibrium strategy. The uniqueness of such equilibrium strategy is also given.