Nonzero-sum stochastic differential games with impulse controls offer a realistic and far-reaching modelling framework for applications within finance, energy markets, and other areas, but the difficulty in solving such problems has hindered their proliferation. Semi-analytical approaches make strong assumptions pertaining to very particular cases. To the author’s best knowledge, the only numerical method in the literature is the heuristic one we put forward in Aïd et al (ESAIM Proc Surv 65:27–45, 2019) to solve an underlying system of quasi-variational inequalities. Focusing on symmetric games, this paper presents a simpler, more precise and efficient fixed-point policy-iteration-type algorithm which removes the strong dependence on the initial guess and the relaxation scheme of the previous method. A rigorous convergence analysis is undertaken with natural assumptions on the players strategies, which admit graph-theoretic interpretations in the context of weakly chained diagonally dominant matrices. A novel provably convergent single-player impulse control solver is also provided. The main algorithm is used to compute with high precision equilibrium payoffs and Nash equilibria of otherwise very challenging problems, and even some which go beyond the scope of the currently available theory.

具有脉冲控制的非零和随机微分博弈为金融，能源市场和其他领域中的应用程序提供了现实且影响深远的建模框架，但是解决此类问题的难度阻碍了它们的扩散。半分析方法针对非常特殊的情况做出了强有力的假设。据作者所知，文献中唯一的数值方法是我们在Aïd等人（ESAIM Proc Surv 65：27-45，2019）中提出的一种启发式方法，用于解决底层的准变分不等式系统。针对对称博弈，本文提出了一种更简单，更精确，更有效的定点策略迭代型算法，该算法消除了对初始猜测的强烈依赖以及先前方法的放松方案。在对玩家策略进行自然假设的情况下进行了严格的收敛分析，该策略接受了在弱链对角优势矩阵的情况下进行的图论解释。还提供了一种新颖的可证明收敛的单玩家脉冲控制求解器。主要算法用于高精度地计算平衡收益和纳什均衡，以解决其他极具挑战性的问题，甚至超出当前可用理论范围的问题。