HO5F10 - (Assume it costs nothing to enter the race The incumbent then has to decide whether she will stay in the race for a month or drop out If

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G AME T HEORY IN THE S OCIAL S CIENCES Political Science 135/Economics 110 Hand Out on Campaign Spending as a (Finite) War of Attrition Many candidates for public office raise large amounts of money for their re-election campaigns even though they are not confronted by a strong challenger. This seems strange. Why would a candidate go through the difficult and unpleasant task of raising a lot of money if he or she is unlikely to be challenged. To examine this situation, consider the following problem. A potential challenger, C , is trying whether he will challenge an incumbent or stay out of the race. The incumbent, I , has a campaign war chest of 3 million dollars to spend on the election whereas the challenger only has 1.5 million dollars. It costs $500,000 a month to stay in the race and a candidate drops out as soon as he or she runs out of money. The game begins with the challenger deciding whether to enter the race or stay out.
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Unformatted text preview: (Assume it costs nothing to enter the race.) The incumbent then has to decide whether she will stay in the race for a month or drop out. If she stays, then the campaign goes on for a month and costs each candidate $500,000. The challenger then has to decide whether he will stay in the race for another month or drop out. If he stays in, both candidates pay an additional $500,000 and at the end of that month the incumbent has to decide what to do. The game continues in this way until one of the candidates drops out or runs out of money. Each candidate prefers winning at lower cost to winning at higher cost; winning at any cost to losing; and losing at lower cost to losing at higher cost. What is the extensive form for this game and the backwards-programming solution? In light of this solution, is it clearer why a candidate might want to amass a large campaign chest?...
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This note was uploaded on 12/25/2010 for the course PO 137 taught by Professor Power during the Fall '10 term at University of California, Berkeley.

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