Zero-sum stopping games with asymmetric information
Optimization and Control
2017-12-06 v3 Probability
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.
Cite
@article{arxiv.1412.1412,
title = {Zero-sum stopping games with asymmetric information},
author = {Fabien Gensbittel and Christine Grün},
journal= {arXiv preprint arXiv:1412.1412},
year = {2017}
}