(3) Elimination of weakly dominated strategies. In this problem we will show that eliminating weakly dominated...

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(3) Elimination of weakly dominated strategies. In this problem we will show that eliminating weakly dominated strategies can change the set of pure Nash equilibria. This is in contrast to what happens when eliminating strictly dominated strategies, which does not change the set of pure equilibria (see the lecture notes). In the following game the additional strategy A was added to matching pennies. H T A H 1,0 0,1 2,0 T 0,1 1,0 1,0 A 1/2,0 0,1 2,2 (a) 10 points. Show that this game has a pure Nash equilibrium. (b) 10 points. What are the weakly dominated strategies? (c) 10 points. Iteratively remove the weakly dominated strategies. What is the resulting game? What are its pure Nash equilibria? (3) Elimination of weakly dominated strategies. In this problem we will show that eliminating weakly dominated strategies can change the set of pure Nash equilibria. This is in contrast to what happens when eliminating strictly dominated strategies, which does not change the set of pure equilibria (see the lecture notes). In the following game the additional strategy A was added to matching pennies. H T A H 1,0 0,1 2,0 T 0,1 1,0 1,0 A 1/2,0 0,1 2,2 (a) 10 points. Show that this game has a pure Nash equilibrium. (b) 10 points. What are the weakly dominated strategies? (c) 10 points. Iteratively remove the weakly dominated strategies. What is the resulting game? What are its pure Nash equilibria?