论文标题
两人零和随机线性二次差异游戏
Two-Person Zero-Sum Stochastic Linear-Quadratic Differential Games
论文作者
论文摘要
该论文研究了开环鞍点和开环的下层和上值，以及它们的关系，其关系具有确定系数的两人零和随机线性季度（LQ，对于简短）差异游戏。它得出了开循环下层和上值的有限性的必要条件，并且有足够的条件对于存在开环鞍点的存在。事实证明，在充分的条件下，对相关的riccati方程的强烈规则解决方案存在独特的存在，在此方面，为开环鞍点进一步建立了闭环表示。示出了示例，以表明开环下值和上值的有限性并不能确保通常存在开环鞍点。但是对于经典的确定性LQ游戏，这两个问题是等效的，都暗示了Riccati方程的解决性，为此获得了解决方案的明确表示。
The paper studies the open-loop saddle point and the open-loop lower and upper values, as well as their relationship for two-person zero-sum stochastic linear-quadratic (LQ, for short) differential games with deterministic coefficients. It derives a necessary condition for the finiteness of the open-loop lower and upper values and a sufficient condition for the existence of an open-loop saddle point. It turns out that under the sufficient condition, a strongly regular solution to the associated Riccati equation uniquely exists, in terms of which a closed-loop representation is further established for the open-loop saddle point. Examples are presented to show that the finiteness of the open-loop lower and upper values does not ensure the existence of an open-loop saddle point in general. But for the classical deterministic LQ game, these two issues are equivalent and both imply the solvability of the Riccati equation, for which an explicit representation of the solution is obtained.
