Zero-sum stopping games with asymmetric information

TL;DR

This paper analyzes a two-player zero-sum stopping game with asymmetric information, where each player observes different Markov chains, establishing the existence of a value, characterizing it, and providing explicit solutions for examples.

Contribution

It introduces a model for zero-sum stopping games with asymmetric information, proving the existence of a value, and offering a variational characterization and explicit solutions.

Findings

Existence of a value in mixed stopping times

Variational characterization of the value function

Explicit solutions for specific examples

Abstract

We study a model of two-player, zero-sum, stopping games with asymmetric information. We assume that the payoff depends on two continuous-time Markov chains (X, Y), where X is only observed by player 1 and Y only by player 2, implying that the players have access to stopping times with respect to different filtrations. We show the existence of a value in mixed stopping times and provide a variational characterization for the value as a function of the initial distribution of the Markov chains. We also prove a verification theorem for optimal stopping rules which allows to construct optimal stopping times. Finally we use our results to solve explicitly two generic examples.