Article

Zero-sum stopping games with asymmetric information

Fabien Gensbittel, and Christine Grün

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.

Replaces

Fabien Gensbittel, and Christine Grün, Zero-sum stopping games with asymmetric information, TSE Working Paper, n. 17-859, November 2017.

Reference

Fabien Gensbittel, and Christine Grün, Zero-sum stopping games with asymmetric information, Mathematics of Operations Research, 2018, forthcoming.

Published in

Mathematics of Operations Research, 2018, forthcoming