Stopper vs. Singular Controller Games With Degenerate Diffusions

Area of Science:

• Stochastic Analysis
• Game Theory
• Optimal Control

Background:

• Investigates zero-sum stochastic games with degenerate diffusion dynamics.
• Standard analytical methods are insufficient due to degenerate dynamics.

Purpose of the Study:

• Establish the existence of a game value for degenerate stochastic games.
• Determine optimal strategies for the stopper in such games.

Main Methods:

• Employs a probabilistic approach using diffusion perturbation.
• Analyzes approximating non-degenerate games for convergence.
• Constructs optimal stopping times for perturbed games.

Main Results:

• Proves the existence of a game value for degenerate stochastic games.
• Identifies an optimal strategy for the stopper.
• Demonstrates convergence of perturbed game values and stopping times.

Conclusions:

• The probabilistic perturbation method successfully addresses degenerate stochastic games.
• Optimal stopping times for the original game are derived from perturbed solutions.