Question

Glassworks and Clearsmooth compete in the local market for windshield repairs. The market size (total available in profits) is $10 million per year. Each firm can choose whether to advertise on local television. If a firm chooses to advertise in a given year, it costs that firm $3 million. If one firm advertises and the other doesn’t, then the former captures the whole market. If both firms advertise, they split the market 50:50. If both firms choose not to advertise, they also split the market 50:50.

1. Display this game in a game table in the space below:

2. What is the Cooperating strategy for each firm? __________________________________________________

3. What is the Defecting strategy for each firm? ____________________________________________________

4. Suppose the two firms know they will compete for just one year. List all Nash equilibria: ________________________________________________________________________________________

5. Suppose the firms play this game for five years in a row, and they know that both firms are quitting the business at the end of the five years. What is the subgame perfect equilibrium for this five-period game? Explain. _________________________________________________________________________________ ________________________________________________________________________________________ ________________________________________________________________________________________

Suppose this game is played for five years in a row, and future profits are discounted with an interest rate of 20% per year.

6. What is the payoff for Glassworks if the Cooperating equilibrium prevails? ________________________________________________________________________________________ ________________________________________________________________________________________

7. Suppose Clearsmooth is playing a Grim Trigger strategy, and Glassworks decides to Defect in year 1. What is Glassworks’ payoff over the five year period? ________________________________________________________________________________________ ________________________________________________________________________________________

a. Should Glassworks Defect in year 1? _______________________________________________________

8. Suppose Clearsmooth is playing a Tit-for-tat strategy, and Glassworks decides to Defect in year 1, then return to Cooperate. What is Glassworks’ payoff over the five year period? ________________________________________________________________________________________ ________________________________________________________________________________________

a. Should Glassworks Defect in year 1? ___________________________________________________

Suppose this game is played for an indefinite period of time. 9. Below what interest rate should Glassworks refrain from Defecting if Clearsmooth is playing a Grim Trigger strategy? ________________________________________________________________________________________ ________________________________________________________________________________________

10. Below what interest rate should Glassworks refrain from Defecting if Clearsmooth is playing a Tit-for-tat strategy? ________________________________________________________________________________________ ________________________________________________________________________________________

Suppose there is a 25% probability (p = 0.25) that the game will continue for another period.

11. What is the effective rate of return? ___________________________________________________________ ________________________________________________________________________________________ a

. Should Glassworks Defect if Clearsmooth is playing a Grim Trigger strategy? Explain ________________________________________________________________________________________

b. Should Glassworks Defect if Clearsmooth is playing a Tit-for-tat strategy? Explain

Answer 1

1. Payoff matrix:

	Clearsmooth
Glassworks	Don't Advertise	Advertise
Don't Advertise	($5 mn,$5 mn)	(0,$10 mn)
Advertise	($10 mn,0)	($5 mn,$5 mn)

2. The Cooperating strategy is for both firms to not advertise and in turn spend 0 as advertising cost while gaining 50% market share each.

3. The Defecting strategy for each firm is to advertise while the other does not. This way the firm that advertises spends $3 mn and gains $10 mn worth of market share, given the other firm does not advertise.

4.

(i) If one of the firms chooses to advertise, the best available option for the other firm is to advertise and gain 50% market share, as opposed to not advertise and have 0 market share. Thus, the point where both firms advertise is a Nash equilibrium point since each firm's strategy is optimal given the other's decision.

(ii) If one of the firms chooses to not advertise, the best available option for the other firm is to advertise and gain 100% market share, as opposed to not advertise and have 50% market share. Thus, there is no Nash equilibrium for this option.