Question

7. Consider the following two player game, with the players being 1 and 2. As usual 1 chooses a row and 2 a column. ABC a 1,4 2,1 3,2 4,1 b 2,3 3,4 4,3 1,2 с 3,1 4,2 1,4 2,3 d 4,2 1,3 4,3 3,2 (a) Which strategies satisfy iterated elimination of strictly dominated strategies? How many levels of knowledge of rationality do you have to assume to obtain your result? (b) If you were allowed to follow the same procedure but iteratively eliminating weakly dominated strategies instead of strictly dominated strategies, what strategies would survive?

Answer 1

a) For player2, strategy C strictly dominates strategy D and no strictly dominated strategy for player 1. Once strategy D of player 2 is eliminated then comparing player1's strategies; b strictly dominates a.

b) There is no weakly dominated strategies for either of the players. The weakly dominated strategies are those which are atleast or higher payoffs compared to some other strategy of the given player while opponent's payoffs are given.