Before revision:  We prove that the superhedging price of a game option{\em  {  coincides with the value function of a corresponding {\em generalized} Dynkin game expressed in terms of the g-evaluation , recently introduced in DQS2 . We then address the case of ambiguity on the model, - for example an ambiguity on the default probability - , and characterize the superhedging price of a game option as the value function of a {\em mixed generalized} Dynkin game.
After revision:  We prove that the superhedging price of a game option{\em { coincides with the value function of a corresponding {\em generalized} Dynkin game expressed in terms of the g-evaluation , recently introduced in DQS2 , expressed with a nonlinear expectation induced by a nonlinear BSDE with default jump. We moreover study the existence of superhedging strategies. We then address the case of ambiguity on the model, - for example an ambiguity on the default probability - , and characterize the superhedging price of a game option as the value function of a {\em mixed generalized} Dynkin game.