2.1 Two firms are planning to sell 10 or 20 units of their goods and face the following profit matrix:

Firm 2 35 50 40 20 60 20 30 30 10 20 Firm 1 10 20 Exercises

a. What is the Nash equilibrium if both firms make their decisions simultaneously?

b. How does your analysis change if the government imposes a lump-sum franchise tax of 40 on each firm 500 CHAPTEr 13 Game Theory Levi Strauss Wrangler White Black Violet White Violet Black 10 30 10 20 0

20 40 20 15 15 35 0 30 30 35 0

40 0

Romano’s 4

0 0 1 4 1 3

3 Do Not Advertise Do Not Advertise Advertise Advertise Giardino’s Thug Safe’s Owner Open the safe, thug does not kill 4 3 Open the safe, thug kills 2 1 Do not open, thug kills 1 2 Do not open, thug does not kill 3 4

(that is, the payoffs in the matrix are all reduced by 40). Explain how your analysis would change if the firms have an additional option of shutting down and avoiding the lump-sum tax rather than producing 10 or 20 units and paying the tax.

c. Draw the game tree if Firm 1 can decide first (and there is no tax). What is the outcome? Why?

d. Draw the game tree if Firm 2 can decide first. What is the outcome? Why?