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Dynkin Games with Incomplete and Asymmetric Information

Author

Listed:
  • 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)

  • Kristoffer Glover

    (University of Technology Sydney, New South Wales 2007, Australia)

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.

Suggested Citation

  • Tiziano De Angelis & Erik Ekström & Kristoffer Glover, 2022. "Dynkin Games with Incomplete and Asymmetric Information," Mathematics of Operations Research, INFORMS, vol. 47(1), pages 560-586, February.
    • Handle: RePEc:inm:ormoor:v:47:y:2022:i:1:p:560-586
    DOI: 10.1287/moor.2021.1141
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