Game theory: Consider the following signaling game, where player one is of type A or type B, each with probability 12 . Player one can go left and right and player two can go up an down. The payoffs are as follows:

a1, a2 A B left, up a C left, down b,0 d, 1 right, up c, 1 a,0 right, down d,0 b, 1