There is, however, a foundational issue that arises here. Suppose that Ann considers it impossible that her opponent will choose action \(a\). Now, there are many reasons why Ann would hold such an opinion. On the one hand, Ann may know something about what her opponent is going to do or is thinking which allows her to rule out action \(a\) as a live possibility—i.e., given all the evidence Ann has about her opponent, she concludes that action \(a\) is just not something her opponent will do. On the other hand, Ann may not even conceive of the possibility that her opponent will choose action \(a\). She may have a completely different model of the game in mind than her opponents. The foundational question is: Can the game models introduced in Section 2 faithfully represent this latter type of uncertainty?