  We consider the superhedging price of an exotic option under nondominated
model uncertainty in discrete time in which the option buyer chooses some
action from an (uncountable) action space at each time step. By introducing an
enlarged space we reformulate the superhedging problem for such an exotic
option as a problem for a European option, which enables us to prove the
pricing-hedging duality. Next, we present a duality result that, when the
option buyers action is observed by the seller up to $l$ periods later, the
superhedging price equals the model-based price where the option buyer has the
power to look into the future for $l$ periods.
