Question 1: Alice and Bob are at a strange auction. The item up for auction is $ 20. The rules are that no one can bid twice in a row and that the highest bidder gets the $ 20. Also, and this is very strange, the highest bidder and the next highest bidder have to pay their bids. For example, if Bob bids $ 5, Alice bids $ 6, and Bob then passes, Alice gets the $ 20 and pays $ 6 to the auctioneer and Bob pays the auctioneer $ 5. Both have $ 100 to bid. What is the optimal strategy?
Question 2:
a) Only two commercial airlines fly from an airport.: Alice Airlines and Bob Airlines. The fly the same route at the same time. It costs each only $ 100 per passenger to fly, no matter how many passengers they fly. The government requires that Alice announce her price and then lets Bob follow her in naming his price. Alice cannot collude with Bob, nor can either change the price once it is announced. Assuming customers have no brand loyalty (that is, they will buy form whoever has the lowest price), what is Alice’s optimal strategy?
b) If in the above question, Alice and Bob can change their fare whenever they want, what fare are they likely to end up charging when the demand curve for seats is Pd = 500 – 0.1Q?
Question 3: A newly married couple find they are playing the following game. Each can choose to invest in the relationship (doing things that make the other person happy) or not. If only one person invests in the relationship, that person is worse off (because all the effort in making the other happy) and the other is better off. The payoff matrix is in utils, a measure of utility. If both invest, the joint payoff is highest (see table below)
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First Term: Husbands Payoff
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WIFE
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|
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Second Term: Wife's Payoff
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Not Invest
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Invest
|
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HUSBAND
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Not Invest
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100, 100
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250, 50
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|
|
Invest
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50,250
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200,200
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a) Which choice makes the couple better off jointly?
b) If this is a noncooperative game, (each person makes an irrevocable choice), what would the outcome be?
c) If this is a cooperative game, what would the outcome be?
d) Suppose divorce is possible. Does it make a difference if divorce requires mutual consent or if divorce is no-fault (where either party can get a divorce without the other’s consent)?
Question 4: Two firms dominate a market. Each faces three choices. They can remain at their same size (not expand), they can make a small expansion, or they can make a large expansion. If both firs make a large expansion, the excess output wipes out their profits. The following shows the payoff matrix:
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First Term: B's Payoff
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Company A
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Second Term: A's Payoff
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Not Expand
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Small Expansion
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Large Expansion
|
|
Company B
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Not Expand
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36,36
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30,40
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18,36
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|
Small Expansion
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40,30
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32,32
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16,24
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|
Large Expansion
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36,18
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24,16
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0,0
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a) What choice will the firms make if they have to commit at the same time (assume they cannot contract with each other)?
b) What choice will they make if Company A makes the first choice and, then, Company B follows