Paper: arXiv 2312.07703

Authors: Tiziano De Angelis, Fabien Gensbittel, Stéphane Villeneuve

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.

Complexity vs Empirical Score

  • Math Complexity: 8.5/10
  • Empirical Rigor: 1.5/10
  • Quadrant: Lab Rats — theoretically deep, empirically untested

Why this score: The paper provides a rigorous mathematical framework for a two-person stochastic game of singular control with absorption, deriving explicit Nash equilibria in feedback form. However, as a purely theoretical corporate finance model, it lacks empirical backtesting, real-world data validation, or quantitative calibration.

Research Flowchart

  flowchart TD
    A[Research Goal: Construct Nash Equilibria for Strategic Dividend Distribution & Default Risk] --> B[Input: Stylized 2-Firm Model with Cash Reserves, Default, & Monopoly Profitability]
    B --> C[Methodology: Stochastic Games of Singular Control with Absorption]
    C --> D[Computational Process: Formulate HJB Variational Inequalities & Randomised Strategies]
    D --> E[Outcome 1: Explicit Optimal Dividend Policies & Equilibrium Payoffs]
    D --> F[Outcome 2: Characterize 2 Types of Equilibria Based on Initial Endowments]