Stochastic nonzero-sum games: a new connection between singular control and optimal stopping

Nash equilibria of threshold type for two-player nonzero-sum games of stopping

This paper analyses two-player nonzero-sum games of optimal stopping on a class of regular diffusions with singular boundary behaviour (in the sense of Itô and McKean (1974) [19], p. 108). We prove that Nash equilibria are realised by stopping the diffusion at the first exit time from suitable intervals whose boundaries solve a system of algebraic equations. Under mild additional assumptions we...

Solving Singular Control from Optimal Switching

This report summarizes some of our recent work (Guo and Tomecek (2008b,a)) on a new theoretical connection between singular control of finite variation and optimal switching problems. This correspondence not only provides a novel method for analyzing multi-dimensional singular control problems, but also builds links among singular controls, Dynkin games, and sequential optimal stopping problems.

Connections between Singular Control and Optimal Switching

This paper builds a new theoretical connection between singular control of finite variation and optimal switching problems. This correspondence provides a novel method for solving high-dimensional singular control problems, and enables us to extend the theory of reversible investment: sufficient conditions are derived for the existence of optimal controls and for the regularity of value functio...

Nonzero-Sum Games of Optimal Stopping for Markov Processes

Nash Equilibrium in Nonzero-Sum Games of Optimal Stopping for Brownian Motion