Question

i K + A B C D W 2,2 5,0 3,6 4,1 X 1,3 2,2 4,5 1,2 Y 3,1 1,1 5,3 6,0 27 DETE 1. (5 points) Find all strictly dominated strategies in this game. 2. (10 points) Find the set of rationalizable strategies for each player. 3. (10 points) Find all the Nash equilibria..

Answer 1

1> For player 2, Y is dominated by X.

For player 1, A is dominated by C

So, the set of Strictly dominated strategy is {A,Y}

2> Rationalizable strategies are those where players are rational and it is a common knowledge that others are. There the strategies which survive after the dominated ones are iteratively eliminated.

After removing A and Y from the game, B dominates D. So, D is removed.

Thus, the set of rationalizable strategies are {B,C,W,X}

3> If B is played. player 2 plays X. If X is played, player 1 plays C. If C is played, player 2 plays W. If W is played, player 1 plays B.

Thus, there is no pure Nash equilibrium in the game

Suppose, player 1 plays pB+(1-p)C, player 2 plays qW+(1-q)X

To remain indifferent, 5q+2(1-q)=3q+4(1-q)

2+3q=4-q

q=0.5

To remain indifferent 6(1-p)=2p+5(1-p)

6-6p=5-3p

p=0.3333

So, the only NE is [1/3B+2/3C,1/2W+1/2X]