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We study the existence of optimal actions in a zero-sum game infτsupPEP[Xτ] between a stopper and a controller choosing the probability measure. We define a nonlinear Snell envelope Y via the theory of sublinear expectations and show that the first hitting time inf{t:Yt=Xt} is an optimal stopping time. The existence of a saddle point is obtained under a compactness condition. (Joint work with Jianfeng Zhang.)

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