Determine the pure strategy nash equilibria, Game Theory

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.

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