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hw8 - 1 h 2 the value of the subsidy that gets approved is...

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ECON 401: Assignment 8 due date: November 30, 2011 1. Consider the all-pay sealed-bid auction: ° one object is for sale; ° there are n bidders and the values are i.i.d. distributed on [0 ; 1] with the cdf function F ( ° ) ; ° bidders submit bids (his price to buy the price) in sealed envelops; ° every bidder pays his bidding price; ° The one bidding the highest price wins the auction, i.e., gets the object; ° Use a fair coin toss to break the tie. What is the symmetric and increasing bidding equilibrium? 2. There are two ±rms in an industry. Each can try to convince Congress to give the industry a subsidy. For i 2 f 1 ; 2 g , let h i denote the number of hours of e/ort put in by ±rm i , and let c i ( h i ) = ( h i ) 2 be the cost of e/ort to ±rm i . When the e/ort levels of the ±rms are ( h
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Unformatted text preview: 1 ; h 2 ) , the value of the subsidy that gets approved is 10 ± ( h 1 + h 2 ) + & ± h 1 ± h 2 , where & ² is a constant. Then, the subsidy well be splitted evenly between the two ±rms. Suppose each ±rm tries to maximize its pro±t, i.e., the subsidy he gets minus the cost of its e/ort. (a) Suppose & = 2 , what are the rationalizable strategies for each ±rm? (b) suppose & = 2 , what are the pure-strategy Nash Equilibria? 3. Suppose we make one modi±cation on Q.1: ±rm 1 moves ±rst, i.e., it chooses h 1 . After observing h 1 , ±rm 2 chooses h 2 . (a) what are the strategies for both ±rms? (b) what are the subgames? (c) suppose & = 2 , what are the Subgame Perfect Nash Equilibria? 1...
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