1. Suppose there are two firms, Firm 1 and Firm 2, who are currently acting in a

Question

1. Suppose there are two firms, Firm 1 and Firm 2, who are currently acting in a competitive manner. Suppose further they have the option of colluding, where both firms agree to raise prices on their customers. Let each firm have two strategies - price their goods high (H) or price them (L). Let the payoffs for each firm be given by the diagram below:

FIRM 1

FIRM 2

H

L

H

$100, $100

$50,$150

L

$150, $50

$60,$60

(a) Solve the game for any Nash equilibria. Show your work. (3 points)

(b) Comment on your answer in (a). (1 point)

(c) Do you think your answer to (a) would change if the firms were located right across the street from one another? Why or why not? (1 point)

FIRM 1

FIRM 2

H

L

H

$100, $100

$50,$150

L

$150, $50

$60,$60

Explanation / Answer

a)In this game, both (H,H) and (L,L) are Nash equilibria. If Firm 1 chooses H then Firm 2 gets 100 by playing H and 150 by playing L. if FIRM 1 chooses L then Player 2 gets 60 by playing L and 50 by playing H. The two stratgies H and L for Firm 1 and the two strategies H and L for Firm 2 are called "pure strategies" and the strategy pairs (H,L) and (H,L) are called "pure strategy equilibria."

b)Nash equilibrium is one of the central solution concepts for games. The basic idea of a Nash equilibrium is that if each player chooses their part of the Nash equilbrium strategy, then no other player has a reason to deviate to another strategy.

c)there is no change in the game from shifting because it depends on the decision of both the firm not on the shift end of firm.

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