🤖 AI Summary
This paper examines a dynamic dividend distribution game between two financially constrained firms competing in a shared market, where default risk generates a monopoly externality—upon one firm’s default, the surviving firm captures the entire market and enjoys higher profits.
Method: We formulate a two-player singular stochastic control game with absorbing boundaries (representing default states) and derive, for the first time, an explicit feedback-type Nash equilibrium using stochastic control theory, Hamilton–Jacobi–Bellman (HJB) equations, and absorption boundary analysis.
Contribution/Results: We obtain closed-form solutions for optimal dividend policies and equilibrium payoffs under two distinct equilibrium regimes: coexistence and dominance. Crucially, we identify a novel mechanism whereby the firms’ initial capital levels endogenously determine the prevailing equilibrium type. The analysis quantifies how competitive market structure simultaneously shapes micro-level financial decisions and macro-level systemic risk.
📝 Abstract
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 focusses 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 randomised 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.