Article

Zero-sum stopping games with asymmetric information

Fabien Gensbittel et Christine Grün

Résumé

We study a model of two-player, zero-sum, stopping games with asymmetric information. We assume that the payoff depends on two independent continuous-time Markov chains, where the first Markov chain is only observed by player 1 and the second Markov chain is only observed 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.

Remplace

Fabien Gensbittel et Christine Grün, « Zero-sum stopping games with asymmetric information », TSE Working Paper, n° 17-859, novembre 2017.

Référence

Fabien Gensbittel et Christine Grün, « Zero-sum stopping games with asymmetric information », Mathematics of Operations Research, vol. 44, n° 1, 2019, p. 277–302.

Publié dans

Mathematics of Operations Research, vol. 44, n° 1, 2019, p. 277–302