Dynkin Games with Incomplete and Asymmetric Information

Tiziano De Angelis (), Erik Ekström () and Kristoffer Glover
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Tiziano De Angelis: University of Torino and Collegio Carlo Alberto, School of Management and Economis, 10134 Torino, Italy
Erik Ekström: Department of Mathematics, Uppsala University, 75106 Uppsala, Sweden

Mathematics of Operations Research, 2022, vol. 47, issue 1, 560-586

Abstract: 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.

Keywords: Primary: 91A15; Secondary: 60G40; 91G10; Dynkin games; asymmetric information; randomised strategies; Nash equilibria; singular control; quasi-variational inequalities (search for similar items in EconPapers)
Date: 2022
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http://dx.doi.org/10.1287/moor.2021.1141 (application/pdf)

Related works:
Working Paper: Dynkin games with incomplete and asymmetric information (2020)
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Persistent link: https://EconPapers.repec.org/RePEc:inm:ormoor:v:47:y:2022:i:1:p:560-586

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