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Dynkin games with incomplete and asymmetric information. (arXiv:1810.07674v1 [math.PR])
来源于:arXiv
We study Nash equilibria for a two-player zero-sum optimal stopping game with
incomplete and asymmetric information. In our set-up, 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 which allows us to find Nash
equilibria by solving suitable quasi-variational inequalities with some
non-standard constraints. Finally, we study an example with linear payoffs, in
which an explicit solution of the corresponding quasi-variational inequalities
can be obtained. 查看全文>>