Dynkin Games with Incomplete and Asymmetric Information

We study the value and the optimal strategies for a two-player zero-sum optimal stopping game with incomplete and asymmetric information. In our Bayesian setup, the drift of the underlying diffusion process is unknown to one player (incomplete information feature), but known to the other one (asymmetric information feature). We formulate the problem and reduce it to a fully Markovian setup where the uninformed player optimises over stopping times and the informed one uses randomised stopping times in order to hide their informational advantage. Then we provide a general verification result that allows us to find the value of the game and players’ optimal strategies by solving suitable quasi-variational inequalities with some nonstandard constraints. Finally, we study an example with linear payoffs, in which an explicit solution of the corresponding quasi-variational inequalities can be obtained.

A MULTIPLEX INTERDEPENDENT DURATIONS MODEL

We propose a multiplex interdependent durations model and study its empirical content. The model considers an empirical stopping game of multiple agents making optimal timing decisions with incomplete information. We characterize the unique Bayesian Nash equilibrium of the stopping game in a system of simultaneous equations involving the conditional distribution of each duration with a moderate strategic interaction condition. The system of nonlinear simultaneous equations allows us to obtain constructive identification results of the interaction effects and other nonparametric model primitives. We propose two consistent semiparametric estimation methods based on different parameterizations of modeling components with right-censored duration data.

A Competitive Optimal Stopping Game

This paper explores a multi-player game of optimal stopping over a finite time horizon. A player wins by retaining a higher value than her competitors do, from a series of independent draws. In our game, a cutoff strategy is optimal, we derive its form, and we show that there is a unique Bayesian Nash Equilibrium in symmetric cutoff strategies. We establish results concerning the cutoff value in its limit and expose techniques, in particular, use of the Budan-Fourier Theorem, that may be useful in other similar problems.