Two Approaches to Non-Zero-Sum Stochastic Differential Games of Control and Stopping

This dissertation takes two approaches - martingale and backward stochastic differential equation (BSDE) - to solve non-zero-sum stochastic differential games in which all players can control and stop the reward streams of the games. Existence of equilibrium stopping rules is proved under some assumptions. The martingale part provides an equivalent martingale characterization of Nash equilibrium strategies of the games. When using equilibrium stopping rules, Isaacs' condition is necessary and sufficient for the existence of an equilibrium control set. The BSDE part shows that solutions to BSDEs provide value processes of the games. A multidimensional BSDE with reflecting barrier is studied in two cases for its solution: existence and uniqueness with Lipschitz growth, and existence in a Markovian system with linear growth rate.

Author dc:creator

• Li, Qinghua

• Mathematical statistics
• Stochastic processes
• Game theory--Mathematical models

Language dc:language

English

DOI dc:identifier

https://doi.org/10.7916/D82R3ZNG

OAI identifier oai:identifier

oai:academiccommons.columbia.edu:10.7916/D82R3ZNG