Robust superhedging duality of exotic multi-action options

We consider a general class of options whose payoff depends on the actions taken by both the seller and the buyer of the option. We call them multi-action exotic options and examples may include basket of American options, or swing options, etc. Then a unified framework is proposedor the robust superhedging duality of the multi-action option with liquid multi-action options available for trading in the hedging portfolio as well. We also incorporate model uncertainty so that the result is robust to model misspecification risk.