Game options, also known as Israeli options are a generalization of American options where the seller has to right to cancel or call back the contract at a prespecified penalty. In this paper, we develop a projected successive overrelaxation algorithm for the valuation of game options under model uncertainty defined by volatility bounds for three scenarios. The first two scenarios are defined when either the buyer or the seller value the options for a worst case scenario and the third scenario values the option when both players are ambiguity averse. The results show the value of the options as non-decreasing in volatility when either player assumes model uncertainty and an increase in the value of the options for larger volatility bounds.