EquilByPretense - Solution by Pretense L A T E X file...

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Unformatted text preview: Solution by Pretense L A T E X file: pretense — Daniel A. Graham <[email protected]>, November 15, 2005 This handout describes a trick commonly used to solve for the symmetric Nash equilibrium in games of incomplete information. To illustrate this method, consider a first-price auction example in which each of two bidders independently and privately draws a valuation for the item to be auctioned from the uniform distribution on [ , 1 ] . Being a game of incomplete information, the equilibrium will take the form of a function, b[v] , having the interpretation that a bidder whose valuation is v will submit bid b[v] . To solve for this function we begin by supposing that it is strictly increasing - this will turn out to be justified - and that one of the players will use this function to submit her bid. For this to be a Nash equilibrium, then it must be the case that the other player can do no better than to use this function to generate his bid as well. If t denotes his true valuation, then he must weakly prefer...
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