Name

1. Everyday Low Prices Bruno Moore and Star Buck are locked in price competition.  Each firm has a choice between two prices for their Mocha Supreme Cappuccino: A normal price (NP) of $6 and a sale price (SP) of $5.  The game matrix for their rivalry appears in the table below.  The payoffs are profits.

		Star
		NP	SP
Bruno	NP	75, 75	75, 85
	SP	85, 75	55, 55

a. Does Bruno have a strictly dominant strategy? Yes No

b. Is the strategy profile <NP_Bruno, NP_Star> an equilibrium? Yes  No

c. What strategy profile maximizes the combined profits of Bruno and Star? NP, NP NP, SP SP, NP SP,SP

d. Is the strategy profile you chose in the previous part an equilibrium for the game? Yes  No

e. How many pure strategy Nash equilibria are there in this game?

f.  What are the pure strategy Nash equilibria? Check all that apply. Bruno's strategy comes first.
  <NP, NP>  <NP, SP>  <SP, NP>  <SP, SP>

g. Are any of the pure strategy Nash equilibria solutions to the game? Yes  No

h. If Bruno plays a mixed strategy, with what probability will he charge the sale price (SP)?  Since the game is symmetric you will also have found the probability with which Star should charge the sale price.

i. If both Bruno and Star play their mixed strategy what is Bruno's expected profit?

j. Based on your answers to this question, would you recommend "low prices everyday" as a marketing strategy for a retailer? Yes  No

2. Mixed Strategies and Best Response In the following game Bruno and Star are choosing among marketing campaigns.  The payoff matrix, in terms of profits, is given below:

		Star
		L	M	R
Bruno	U	8, 1	0, 2	4, 3
	C	3, 1	4, 4	0, 0
	D	5, 0	3, 3	1, 4

a. Does Star have a dominant strategy? Yes  No

b. Does Bruno have a dominant strategy? Yes  No

c. Does Star have a dominated strategy?  Yes  No

d. Does Bruno have a dominated strategy? Yes  No

e. Does Star have a strategy that she would not use as a best response? If so, what is it? Yes, L Yes, M Yes, R No

f. Does Bruno have a strategy that he would not use as a best response? If so, what is it? Yes, U Yes. C Yes, D No.

g. Suppose Star plays a mixed strategy.  Enter the probabilities with which she plays each of her strategies.
      L:    M:    R: 

h. Suppose Bruno plays a mixed strategy.  Enter the probabilities with which he plays each of his strategies.
      U:    C:     D: 

i. Is there a strategy that Star will not play as part of her strategic plan? Yes, L. Yes, M. Yes, R. She plays them all.

j. Is there a strategy that Bruno will not play as part of his strategic plan? Yes, U Yes, M Yes, D He plays them all.