a) Define the term Nash equilibrium
b) You are given the following pay-off matrix:
|
Strategies for player 1
|
|
Strategies for player 2
|
|
L
|
C
|
R
|
|
T
|
2,0
|
1,1
|
4,2
|
|
M
|
3,4
|
1,2
|
2,3
|
|
B
|
1,3
|
0,2
|
3,0
|
i) What strategies survive the iterated elimination of strictly dominated strategies?
ii) What are the pure-strategy Nash equilibria of this game?
c) A Cournot duopoly has a demand function of the form p (Q)=a-Q and faces a marginal cost C>0 where a>c . Determine the profit maximizing output for each firm and the optimal price.
d) If the two firms in (a) were to merge to form a monopoly, what would be the profit-maximizing output and the corresponding price? Compare both the output and price under Cournot and monopolist.