1. Bruster\'s and Rita\'s both sell equally delicious ice cream, and compete for
ID: 1139327 • Letter: 1
Question
1. Bruster's and Rita's both sell equally delicious ice cream, and compete for the same customers. Each can offer customers a rewards card (offering free ice cream after certain number of purchases), or not. Profits at each firm are greater if neither firm offers a rewards card than if both do. If one firm offers a rewards card and the other doesn't, the one offering the rewards card earns higher profits than in the case where neither firm offers a reward card, while the firm that does not offer a rewards card earns lower profits than in the case where both firms offer a rewards card. a. Choose some profit numbers (payoffs) for this game that are consistent with the description above and write the game matrix. b. Does either player have a dominant strategy in this game? If so, what is it? game in normal form. Be sure to label the strategies and players in your Suppose that Pat and Sam intended to communicate with each other about what to do tonight but the message never got through. Now each has to simultaneously and independently decide where to show up (communication is no longer possible). There are just two possibilities-a ball game or a concert. Other things equal, Pat likes ball games better, and Sam likes concerts better. Both Pat and Sam agree that either event would be more fun if the other person were also there. However, Pat and Sam differ in their attitudes about how important it is that they be there together. Since Pat is choosing between the game or the concert and Sam is facing the same two choice, there are four possible outcomes. The table below shows how Sam and Pat rank these four outcomes, Outcome 2. Sam s Kankin Sam at concert, Pat at concert Sam at game, Pat at game Sam at concert, Pat at game Sam at game, Pat at concert Second Best Worst a. Write down the normal form of this game (i.e., game matrix). Choose payoffs that are consistent with the rankings given in the table above. Assume there are no ties (e.g. "best" is strictly better than "second best", which is strictly better than "third best" which is strictly better than "worst"). b. Find all pure strategy Nash equilibria for this game. Does either player have a dominant strategy? Pat at concert, Sam at gameExplanation / Answer
Answer 1.
Bruster’s and Rita’s both have two possible strategies/ choices – To offer a reward card or To not offer a reward card.
THE NORMAL FORM FOR THE GAME IS AS FOLLOWS:
RITA’S
BRUSTER’S
Offer a rewards card
Do not Offer a rewards card
Offer a rewards card
(500,500)
(1500,250)
Do not Offer a rewards card
(250,1500)
(1000,1000)
b)Both players have a dominant strategy of- offer a rewards card.
- If Bruster’s offer a rewards card, Rita earns more profit by offering a rewards card ($500>$250)
- If Bruster’s do not offer a rewards card, Rita earns more profit by offering a rewards card ($1500>$1000)
- Same for Rita’s also, as payoffs are symmetric.
RITA’S
BRUSTER’S
Offer a rewards card
Do not Offer a rewards card
Offer a rewards card
(500,500)
(1500,250)
Do not Offer a rewards card
(250,1500)
(1000,1000)
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