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 firstprice 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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 Spring '09
 Physics, Game Theory, Probability theory, Auction

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