# lecture16 - Lecture XVI: Auctions Markus M. Mobius May 6,...

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Unformatted text preview: Lecture XVI: Auctions Markus M. Mobius May 6, 2004 Gibbons, chapter 3 Osborne, chapter 9 Paul Klemperers website at http://www.paulklemperer.org/ has fan- tastic online material on auctions and related topics. 1 Introduction We already introduced a private-value auction with two bidders last time as an example for a game of imperfect information. In this lecture we expand this definition a little bit. In all our auctions there are n participants and each participant has a valuation v i and submits a bid b i (his action). The rules of the auction determine the probability q i ( b 1 ,..,b n ) that agent i wins the auction and the expected price p i ( b 1 ,..,b n ) which he pays. His utility is simple u i = q i v i- p i . a a The agent is risk-neutral - new issues arise if the bidders are risk-averse. There are two important dimensions to classify auctions which are based on this template: 1 1. How are values v i drawn? In the private value environment each v i is drawn independently from some distribution F i and support [ v , v ]. For our purposes we assume that all bidders are symmetric such that the v i are i.i.d. draws from a common distribution F . 1 In the correlated private value environment the v i are not independent - for example if I have a large v i the other players are likely to have a large value as well. In the pure common value environment all bidders have the same valuation v i = v j . 2 2. What are the rules? In the first price auction the highest bid wins and the bidder pays his bid. In the case of a tie a fair coin is flipped to determine the winner. 3 In the second price auction the highest bidder wins but pays the second-highest bid. In the all-pay auction all bidders pay and the highest bidder wins. All these three auctions are static games. The most famous dynamic auction is the English auction where the price starts at zero and starts to rise. Bidders drop out until the last remaining bidder gets the auction. 4 The Dutch auction is the opposite of the English - the price starts high and decreases until the first bidder jumps in to buy the object. The Dutch auction is strategically equivalent to the first-price auction. Note, that in May 2004 Google decided to use a Dutch auction for its IPO. We will usually assume symmetric private value environments. 1 Typically we assume that the distribution is continuous and has no atoms. 2 There are much more general environments. A very general formulation which en- compasses both private and common value auctions is due to Wilson (1977). Each bidder gets a signal t i about her valuation which is drawn from some distribution g i ( t i ,s ) where s is a common noise term for all players. The players value is then a function v ( t i ,s ). If v i = t i we get back the private value environment. Similarly, if v i = v ( s ) we have the pure common value environment....
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## This note was uploaded on 05/19/2010 for the course DFDAS 220 taught by Professor Ding during the Fall '10 term at Academy of Art University.

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lecture16 - Lecture XVI: Auctions Markus M. Mobius May 6,...

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