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arXiv · 2607.08861

Convergence of fictitious play for fully coupled FBSDEs in finite-player stochastic differential games

Adam Andersson·Kristoffer Andersson·Per Ljung
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Abstract

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.

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Adam Andersson, Kristoffer Andersson, Per Ljung. 2026-07-09. Convergence of fictitious play for fully coupled FBSDEs in finite-player stochastic differential games. https://arxiv.org/abs/2607.08861

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