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week 2 1 COS 444 Internet Auctions: Theory and Practice Spring 2008 Ken Steiglitz ken@cs.princeton.edu
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week 22 Praxis Cassady on executing the (English) bid Cassady on executing the (English) bid Book bids, anticipating eBay Book bids, anticipating eBay Mail-bid sales Mail-bid sales Buy-or-Bid sales (cf Buy-It-Now on eBay) Buy-or-Bid sales (cf Buy-It-Now on eBay) Ticks (= increments) Ticks (= increments)
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week 23 Theory: the four basic auctions English weakly equivalent to Vickrey Dutch strategically equivalent to FP
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week 24 Theory: truthful bidding Truthful bidding is weakly dominant in Vickrey auctions Truthful bidding is weakly dominant in Vickrey auctions Truthful bidding is also weakly dominant Truthful bidding is also weakly dominant in (Japanese button) English auctions, but not in ascending-price or outcry English auctions in (Japanese button) English auctions, but not in ascending-price or outcry English auctions
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week 25 Theory: probability pdf pdf cdf cdf Expectation Expectation
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week 26 Theory: probability Almost universal assumption: range normalized to [0,1] Almost universal assumption: range normalized to [0,1] Common assumption for examples, etc., v ’s “uniformly distributed on [0,1]”, which means Common assumption for examples, etc., v ’s “uniformly distributed on [0,1]”, which means f (x ) = 1, F (x ) = x f (x ) = 1, F (x ) = x and iid = “independently and identically distributed” and iid = “independently and identically distributed”
![week 26 Theory: probability Almost universal assumption: range normalized to [0,1] Almost universal assumption: range normalized to [0,1] Common assumption for examples, etc., v ’s uniformly distributed on [0,1] , which means Common assumption for examples, etc., v ’s uniformly distributed on [0,1] , which means f (x ) = 1, F (x ) = x f (x ) = 1, F (x ) = x and iid = independently and identically distributed and iid = independently and identically distributed](http://images.slideplayer.com/16/4924820/slides/slide_6.jpg "week 26 Theory: probability Almost universal assumption: range normalized to [0,1] Almost universal assumption: range normalized to [0,1] Common assumption for examples, etc., v ’s uniformly distributed on [0,1] , which means Common assumption for examples, etc., v ’s uniformly distributed on [0,1] , which means f (x ) = 1, F (x ) = x f (x ) = 1, F (x ) = x and iid = independently and identically distributed and iid = independently and identically distributed")
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week 27 Praxis Disincentives to truthful bidding Disincentives to truthful bidding Evolution of eBay from mail-bid sales (conceptually anyway) Evolution of eBay from mail-bid sales (conceptually anyway) The "California auction" as an abstraction The "California auction" as an abstraction Other online closing rules, Amazon & Yahoo Other online closing rules, Amazon & Yahoo Taobao, the Chinese online auction site? Taobao, the Chinese online auction site?
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week 28 Theory: simplest RE Back to n=2 bidders, uniform iid v ’s Back to n=2 bidders, uniform iid v ’s E[pay] in SP, when bidders bid truthfully, is average second-price E[pay] in SP, when bidders bid truthfully, is average second-price = 1/3 (to be proved shortly) = 1/3 (to be proved shortly) E[pay] in FP at equilibrium is E[pay] in FP is average of this over v 1 = 1/6 times 2 bidders = 1/3 … same as SP E[pay] in FP is average of this over v 1 = 1/6 times 2 bidders = 1/3 … same as SP
![week 28 Theory: simplest RE Back to n=2 bidders, uniform iid v ’s Back to n=2 bidders, uniform iid v ’s E[pay] in SP, when bidders bid truthfully, is average second-price E[pay] in SP, when bidders bid truthfully, is average second-price = 1/3 (to be proved shortly) = 1/3 (to be proved shortly) E[pay] in FP at equilibrium is E[pay] in FP is average of this over v 1 = 1/6 times 2 bidders = 1/3 … same as SP E[pay] in FP is average of this over v 1 = 1/6 times 2 bidders = 1/3 … same as SP](http://images.slideplayer.com/16/4924820/slides/slide_8.jpg "week 28 Theory: simplest RE Back to n=2 bidders, uniform iid v ’s Back to n=2 bidders, uniform iid v ’s E[pay] in SP, when bidders bid truthfully, is average second-price E[pay] in SP, when bidders bid truthfully, is average second-price = 1/3 (to be proved shortly) = 1/3 (to be proved shortly) E[pay] in FP at equilibrium is E[pay] in FP is average of this over v 1 = 1/6 times 2 bidders = 1/3 … same as SP E[pay] in FP is average of this over v 1 = 1/6 times 2 bidders = 1/3 … same as SP")
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