Exercise 1: Iterated Elimination of Strictly Dominated Actions
Consider a strategic game with two players. Player 1’s set of actions is S1 = {A, B, C, D} and player 2’s set of actions is S2 = {S, T, U, V}. The players’ payoffs are displayed in the payoff matrix below.
Payoffs u1, u2
A B C D
Player 2
S 4,4 2,10 3,7 5,4
T 10,9 4,10 5,9 9,5
U 4,6 7,6 10,6 5,8
V 8,7 12,2 4,5 4,4
Use the procedure of iterated elimination of strictly dominated actions to identify the set of all action profiles that survive iterated elimination of strictly dominated actions.
• In each stage t = 1, . . . , T, clearly list the action sets for all players, Xit (i in {1, 2}), and explain how you determined Xt based on Xt−1. Provide the (reduced) payoff matrix for each stage.
• Reminder (Definition 45.1): In a strategic game with ordinal preferences, player i’s action a′′ strictly dominates her action a′ if u(a′′, a) > u(a′, a). We say that the action a′i is strictly dominated.