Before revision:  That is, \pi=(c_i,Q_i)_i\sum_ic_i\phi^{Q_i}, where c_i \in   _+ and the martingale measure Q^i are chosen such that \sum_i c_i=1 and \sum_i c_iQ_i prices the European options correctly, and \phi^{Q_i} is the price of the American option under the model Q_i  .
After revision:  That is, \pi=(c_i,Q_i)_i\sum_ic_i\phi^{Q_i}, where c_i \in  _+ and the martingale measure Q^i are chosen such that \sum_i c_i=1 and \sum_i c_iQ_i prices the European options correctly, and \phi^{Q_i} is the price of the American option under the model Q_i . Our result generalizes the example given in ArXiv:1604.02274 that the highest model based price can be considered as a randomization over models .