Lecture6_103 - Econ 103C-Lecture 6 An introduction to Auction Theory David Sraer Berkeley University David Sraer(Berkeley University Econ

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Unformatted text preview: Econ 103C-Lecture 6 An introduction to Auction Theory David Sraer Berkeley University April 21, 2008 David Sraer (Berkeley University) Econ 103C-Lecture 6 April 21, 2008 1 / 30 Some common auction forms Open ascending price auction (or English auction) Open descending price auction (or Dutch auction): not commonly used in practice. Sealed bid first price auction. Sealed bid second price auction → ebay! David Sraer (Berkeley University) Econ 103C-Lecture 6 April 21, 2008 2 / 30 Valuations Auctions are used because the seller ignores the values that bidders attach to the object! Question: design a mechanism to overcome this informational issue when only 1 item is sold? Two situations: 1 The bidder knows the value of the object to himself at the time of bidding → private values. Ex: a CD on ebay! 2 Each bidder only have an imperfect value of the true common value of the object → common values. Ex: bidding for an oil field. David Sraer (Berkeley University) Econ 103C-Lecture 6 April 21, 2008 3 / 30 Evaluating auctions Two grounds on which to evaluate auctions: Revenue: How much utility does a particular auction provide the seller of the good with? Efficiency: does the object fall in the hand of the agent with the highest utility for it? David Sraer (Berkeley University) Econ 103C-Lecture 6 April 21, 2008 4 / 30 What is an auction? Two important general characteristics of auctions: Auctions are mechanisms that elicit information, in the form of bids , from potential buyers of a good regarding their willingness to pay and the outcome is determined solely on the basis of the received information → “universality” In an auction, the identity of the bidder plays no role in determining who wins the object and who pays how much → “anonymity” David Sraer (Berkeley University) Econ 103C-Lecture 6 April 21, 2008 5 / 30 The formal framework (1) There is a single object for sale. There are N potential buyers/bidders. Each bidder i ∈ [1 , N ] is willing to pay x i for the object at most. Each x i corresponds to the realization of a random variable X i , which is i.i.d on some interval [0 ,ω ] according to the increasing distribution function F , continuous and with full support. E [ X ] < ∞ David Sraer (Berkeley University) Econ 103C-Lecture 6 April 21, 2008 6 / 30 The formal framework (2) Bidder i knows only the realization x i of his own valuation and simply knows that others’ valuation are drawn i.i.d. from F . Bidders are risk-neutral. All components of the model other than the realized values are commonly known to all bidders. There are no liquidity/budget constraints: each bidder can pay up to his/her value x i David Sraer (Berkeley University) Econ 103C-Lecture 6 April 21, 2008 7 / 30 Analysis of second price auctions (1) Call β i : [0 ,ω ] 7→ R + the equilibrium bid function of bidder i ....
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This note was uploaded on 08/01/2008 for the course ECON 103C taught by Professor Sraer during the Spring '08 term at University of California, Berkeley.

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Lecture6_103 - Econ 103C-Lecture 6 An introduction to Auction Theory David Sraer Berkeley University David Sraer(Berkeley University Econ

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