Let x 4 and y 3 What do you get when you apply the procedu

Let x = 4 and y = 3. What do you get when you apply the procedure of iterative elimination of strictly dominated strategies? Write explicitly the various steps of the elimination procedure.

Consider the following game ( and y can be any r the following game (r and y can be any non-negative real numbers): Player 2 A2,4 2, 3 3, 4 4 , 2 3 , 4 3 , 2 0, 3 2, y 0,1 C3, 2 Dx . 3

Solution

Given the above pay offs and x= 4 and y=3 , by the process of iterative elimination of strictly dominated strategies we can eliminate strategy A , B AND E for player 1 because his pay offs in these strategies are lower whatever strategy is adopted by player2.After eliminating these our game becomes

However for player 2 strategy F and G are the strictly dominated strategies as player 2\'s pay off in playing H is higher.Thus strategies F and G are eliminated for player 2.Thus our new game becomes

Now for player 1 clearly strategy D is strictly dominated by strategy C as his pay off is higher in C.Thus eliminating D for player1 we remain with strategy C for player 1 and strategy H for player 2.Thus the pay off when player 1 plays C and player 2 plays H is (2,3).

	F	G	H
C	3,2	4,2	2,3
D	4,3	3,4	1,4