有限参与者随机微分博弈中完全耦合正倒向随机微分方程的虚拟策略收敛性
Convergence of fictitious play for fully coupled FBSDEs in finite-player stochastic differential games
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中文总结 AI 辅助
研究有限参与者随机微分博弈中完全耦合正倒向随机微分方程的虚拟策略收敛性，在一定假设下证明其收敛为几何收敛，特殊博弈中为超指数收敛，通过线性二次型银行间借贷问题数值实验予以证实。
中文摘要 AI 辅助
本文研究了将虚拟策略逼近过程应用于有限参与者非零和随机微分博弈的耦合正倒向随机微分方程系统的理论收敛性质。在一组假设下，收敛被证明是几何收敛。在一个额外的结构假设下，在一类特殊博弈中几何收敛速率进一步提高到超指数速率。据我们所知，这首次对完全耦合正倒向随机微分方程的虚拟策略进行了收敛分析。一个线性二次型银行间借贷问题的数值实验证实了几何收敛。
英文摘要
In this article we investigate the theoretical convergence properties of the fictitious-play approximation procedure applied to coupled FBSDE systems for finite-player non-zero-sum stochastic differential games. Under one set of assumptions, the convergence is shown to be geometric. Under an additional structural assumption, the geometric convergence rate further improves to a super-exponential rate in a special class of games. To the best of our knowledge, this provides the first convergence analysis of fictitious play for fully coupled FBSDEs. A numerical experiment with a linear-quadratic interbank borrowing and lending problem confirms the geometric convergence.
