The key idea is to represent the players’ beliefs as a lexicographic probability system (LPS). An LPS is a finite sequence of probability measures \((p_1,p_2,\ldots,p_n)\) with supports (The support of a probability measure \(p\) defined on a set of states \(W\) is the set of all states that have nonzero probability; formally, \(Supp(p)=\{w \mid p(w)&gt;0\}\)) that do not overlap. This is interpreted as follows: if \((p_1,\ldots,p_n)\) represents Ann’s beliefs, then \(p_1\) is Ann’s “initial hypothesis” about what Bob is going to do, \(p_2\) is Ann’s secondary hypothesis, and so on. In the above game, we can describe Bob’s beliefs as follows: his initial hypothesis is that Ann will choose \(U\) with probability 1 and his secondary hypothesis is that she will choose \(D\) with probability 1. The interpretation is that, although Bob does not rule out the possibility that Ann will choose \(D\) (i.e., choose irrationally), he does consider it infinitely less likely than her choosing \(U\) (i.e., choosing rationally).