On a filtered probability space (\Omega,\mathcal{F,P,F=(F_t)_{0\leq t\leq T}), we consider stopper-stopper games }%DIFDELCMD < \bar %%% C:=\inf_{\Rho\tau\in\T}%DIFDELCMD < \E[U(\Rho(\tau),\tau)] %%% and%DIFDELCMD < \underline %%% C:=\sup_{\Tau\rho\in\T}%DIFDELCMD < \E[U(\Rho(\tau),\tau)] %%% in continuous time , where U(s,t) is \mathcal{F_{s\vee t}-measurable (this is the new feature of our stopping game ), }%DIFDELCMD < \T %%% is the set of stopping times, and%DIFDELCMD < \Rho%%% ,%DIFDELCMD < \Tau%%% :%DIFDELCMD < \T%%% \mapsto%DIFDELCMD < \T %%% satisfy certain non-anticipativity conditions. We show that%DIFDELCMD < \bar %%% C=%DIFDELCMD < \underline %%% C, by converting these problems into a corresponding Dynkin game  .
,P,F=(F_t)_{0\leq t\leq T}), we consider stopper-stopper games }%DIFDELCMD < \bar %%% \tau\in\T}%DIFDELCMD < \E[U(\Rho(\tau),\tau)] %%% %DIFDELCMD < \underline %%% \rho\in\T}%DIFDELCMD < \E[U(\Rho(\tau),\tau)] %%% _{s\vee t}-measurable (this is the new feature of our stopping game ), }%DIFDELCMD < \T %%% We consider a zero-sum continuous time stopping %DIFDELCMD < \Rho%%% %DIFDELCMD < \Tau%%% %DIFDELCMD < \T%%% %DIFDELCMD < \T %%% %DIFDELCMD < \bar %%% %DIFDELCMD < \underline %%% game in which the pay-off is revealed in the maximum of the two stopping times instead of the minimum, which is the case in Dynkin games .
D
On a filtered probability space (\Omega,\mathcal{F
D
C:=\inf_{\Rho
D
and
D
C:=\sup_{\Tau
D
in continuous time , where U(s,t) is \mathcal{F
R
is the set of
We consider a zero-sum continuous time
D
times, and
D
,
D
:
D
\mapsto
D
satisfy certain non-anticipativity conditions. We show that
D
C=
D
C, by converting these problems into a corresponding Dynkin
A
in which the pay-off is revealed in the maximum of the two stopping times instead of the minimum, which is the case in Dynkin games