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Unformatted text preview: Problem Set 9. Econ 159a/MGT522a Ben Polak Three Problems (and one optional problem) due November 28, 2007 1. War of Attrition. In the two-stage war of attrition we studied in class, we focussed on the case where v > c . For the converse case c > v , &nd all the sub-game perfect equilibria, pure and mixed, including equilibria in which players mix in the &rst stage but do not mix in the second. [Hint: be careful when calculating the mixing probabilities to take account of what will happen in stage 2]. 2 . \It’s a Wonderful Life" . Arnold and Boris have each deposited the same amount, $ D , into the Smalltown Saving and Loan (S¡L). Since Arnold and Boris are the only two investors, the initial total in the S¡L is $2 D . Money in the S¡L grows over time: perhaps, the nice manager of the S¡L invests it in local people’s businesses and housing. By period 1, the total money in the S¡L will increase to 2 r . If the S¡L survives to period 2, the money will increase to 2 R . Assume R > r > D . In period 1, each depositor can either withdraw or not-withdraw his money. (He cannot withdraw just part of it). These choices are made simultaneously. If either of them withdraws, the S¡L goes bust. If just one person withdraws in period 1, the withdrawer gets $(2the S¡L goes bust....
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This note was uploaded on 02/13/2012 for the course ECON 159 taught by Professor Benjaminpolak during the Fall '08 term at Yale.
- Fall '08
- Game Theory