Control-Stopping Games for Market Microstructure and Beyond

We present a family of a control-stopping games which arise naturally in equilibrium-based models of market microstructure, as well as in other models with strategic buyers and sellers. In such a game, an agent can always stop... [ view full abstract ]

We present a family of a control-stopping games which arise naturally in equilibrium-based models of market microstructure, as well as in other models with strategic buyers and sellers. In such a game, an agent can always stop the game by executing a trade at the bid or ask price quoted by the other agent. The equilibria are described by a system of coupled control-stopping problems, or, equivalently, by a system of RBSDEs with oblique reflection. We describe the associated mathematical challenges and prove existence of a solution to this system.