We construct Nash equilibria in feedback form for a class of two-person stochastic games of singular control with absorption, arising from a stylized model for corporate finance. More precisely, the paper focuses on a strategic dynamic game in which two financially constrained firms operate in the same market. The firms distribute dividends and are faced with default risk. The strategic interaction arises from the fact that if one firm defaults, the other one becomes a monopolist and increases its profitability. The firms choose their dividend distribution policies from a class of randomized strategies, and we identify two types of equilibria, depending on the firms’ initial endowments. In both situations, the optimal strategies and the equilibrium payoffs are found explicitly. Funding: T. De Angelis was partially supported by PRIN2022 project ID BEMMLZ Stochastic Control and Games and the Role of Information. Part of the research was conducted while S. Villeneuve was visiting Collegio Carlo Alberto in Torino, under a fellowship granted by LTI@UniTO. F. Gensbittel received financial support from ANR Programmes d’Investissements d’Avenir CHESS ANR-17-EURE-0010 and ANITI ANR-19-PI3A-0004.
Angelis et al. (2025) studied this question.