PS6-solutions

PS6-solutions - Suggested Solutions to Problem Set 6 ECN...

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Suggested Solutions to Problem Set 6 ECN 416 Game Theory 1 . Suppose you are trying to buy a house and you are bargaining with the current owner over the sale price. The house is worth $200 000 to you and $100 000 to the current owner. So if the price is between $100 000 and $200 000 , then you would both be better o f with the sale. Assume the bargaining takes place with alternate o f ers and that each stage of bargaining (an o f er and a response) takes a full day to complete. If agreement is not reached after 5 days of bargaining, then the opportunity for the sale disappears (you will have no house and the current owner has to keep the house forever). Suppose that you and the current owner discount the future according to the discount factor per day. The real estate agent has allowed you to decide whether or not you shall make the f rst o f er. (a) Suppose that is small. In particular  1 2 . Should you make the f rst o f er or let the current owner make the o f er?Why? Asshowninclass,ifyoumakethe f rst o f er, then your equilibrium payo f is 1 5 1+ and if let the other party make the f rst o f er, then your equilibrium payo f is ³ 1 1 5 1+ ´ = + 5 1+ .Soi f  1 2 ,then 1 5 1+ + 5 1+ and you are better o f making the f rst o f er. (b) Suppose that is close to 1 ;inpart icu lar 5 1 2 . Should you make the f rst o f er or let the current owner make the f rst o f er? Why? If 5 1 2 ,then 1 5 1+ + 5 1+ and you should let the current owner make the f rst o f er. 2. Consider the following discounted, three period bargaining game. The players divide $1 . The common discount factor is ,where 0  1 . In this game, player 1 makes the f rst o f er. If player 2 rejects this o f er, then player 1 makes another o f er. If player 2 rejects the second o f er, then player 2 makes the f nal o f er. If no o f er is accepted at the end, both players get
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PS6-solutions - Suggested Solutions to Problem Set 6 ECN...

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