Game Theory de Drew Fudenberg, Jean Tirole.

Exercise 2.6**

14259, au ovyurulia LLLLLLLS VILIVY piam.15.) Exercise 2.6** Consider the two-player game in figure 2.7. This is match- ing pennies with an outside option a for player 1. Suppose that a E (0,1). (a) Show that the set of mixed strategies for player 1 surviving iterated deletion of strictly dominated strategies consists of two "edges of the strategy simplex": the set of mixed strategies with support (H,Q) and the set of mixed strategies with support (T,). (b) Show directly (that is, without applying theorem 2.2) that the set of rationalizable strategies for player 1 is also composed of these two edges. (Hint: Use a diagram similar to figure 2.3.) H 1.-1 -1,1 T -1,1 1,-1 a a, o a, o Figure 2.7 14259, au ovyurulia LLLLLLLS VILIVY piam.15.) Exercise 2.6** Consider the two-player game in figure 2.7. This is match- ing pennies with an outside option a for player 1. Suppose that a E (0,1). (a) Show that the set of mixed strategies for player 1 surviving iterated deletion of strictly dominated strategies consists of two "edges of the strategy simplex": the set of mixed strategies with support (H,Q) and the set of mixed strategies with support (T,). (b) Show directly (that is, without applying theorem 2.2) that the set of rationalizable strategies for player 1 is also composed of these two edges. (Hint: Use a diagram similar to figure 2.3.) H 1.-1 -1,1 T -1,1 1,-1 a a, o a, o Figure 2.7