Question

Find the Nash equilibria of and the set of rationalizable strategies for the games

2 2 L R L С R 3,3 2,0 A 5,9 0, 1 U 4,3 В 4,1 8,- 3,2 М 0,9 1,1 D 0,1 2, 8 8,4 (а) (b) 2 2 1 W X Y Z R 3,6 4, 10 5,0 U 0,8 U 0,0 1, 1 2,6 3, 3 4, 10 1,1 0,0 5,5 D 1,5 2,9 3,0 4,6 (d) (c) L M

Answer 1

la)

Player 1:

Strategy B is dominant strategy for player 1: (4,8) > (3,2)

Player 2:

Strategy L is a dominant strategy for player 2: ( 3, 1) > (0, -1)

Hence, both will go with their dominant strategies.

Nash equilibrium: ( B:L)

b)

Player 1)

Strategy M has been weakly dominated by strategy U. Thus, M must be eliminated.

Player 2)

R has been dominated by the L. So R will be eliminated.

When M is deleted, the Player 2 is left with a strategy L

If player 2 selects the strategy L, only U will be selected.

Nash Equilibrium: ( U,L)

c)

Player 1)

Player 1 selects	Player 2 responds
U	X
M	Y
D	X

Player 2 selects	Player 1 responds
W	U
X	U
Y	U
Z	D

Common Response is X, U.

Hence, it would be Nash Equilibrium: ( X,U)

d)

It clear from table that there are two Nash equilibrium in this game.

common response would be : (U,L) , (D,R)

Nash Equilibrium: ( U,L) and (D,R)