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
Player 1
S A 4, 4 2, 10 3, 7 D 5, 4
T 10, 9 9, 5 10, 6
Player 2
U 4, 10 4, 6 5, 8 4, 5
V 5, 9 7, 6 8, 7 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, X(i ∈ {1,2}), and explain how you determined X based on X!-'. 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_i) > u(a,, a_i) for every list a_; of the other players' actions. We say that the action a' is strictly dominated.