Convergence of fictitious play for fully coupled FBSDEs in finite-player stochastic differential games
Provides the first convergence analysis of fictitious play for fully coupled FBSDEs, relevant for game theory and stochastic control.
The paper proves geometric convergence of fictitious play for fully coupled FBSDEs in finite-player stochastic differential games, with super-exponential rates under additional assumptions, confirmed numerically.
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.