![Page 1: Game Theory Applications: Lecture Notesciti.umich.edu/u/galka/games/Lauctions.pdf · Game Theory Applications: Lecture Notes ... 04.16.01 and 04.18.01 Lecture Notes in Game Theory](https://reader034.vdocuments.us/reader034/viewer/2022052608/5a9e18827f8b9a29228d878f/html5/thumbnails/1.jpg)
04.16.01 and 04.18.01 Lecture Notes in Game Theory 1
Game Theory Applications: Lecture Notes
Course Websitehttp://www.citi.umich.edu/u/galka/games
u Galina Albert Schwartzu Department of Financeu University of Michiganu Business School
![Page 2: Game Theory Applications: Lecture Notesciti.umich.edu/u/galka/games/Lauctions.pdf · Game Theory Applications: Lecture Notes ... 04.16.01 and 04.18.01 Lecture Notes in Game Theory](https://reader034.vdocuments.us/reader034/viewer/2022052608/5a9e18827f8b9a29228d878f/html5/thumbnails/2.jpg)
04.16.01 and 04.18.01 Lecture Notes in Game Theory 2
Summary of last two lectures
u Auctions: Dixit, chapter 15u Types of Auctionsu Winner’s Curseu Vickrey’s Theoremu Auction Designu Summary of the Course
![Page 3: Game Theory Applications: Lecture Notesciti.umich.edu/u/galka/games/Lauctions.pdf · Game Theory Applications: Lecture Notes ... 04.16.01 and 04.18.01 Lecture Notes in Game Theory](https://reader034.vdocuments.us/reader034/viewer/2022052608/5a9e18827f8b9a29228d878f/html5/thumbnails/3.jpg)
04.16.01 and 04.18.01 Lecture Notes in Game Theory 3
Auction Design: Types of Auctions
u Four Major Considerations– Types of Auction Settings– Bidding Types– Pricing Schemes– Valuation Methods
![Page 4: Game Theory Applications: Lecture Notesciti.umich.edu/u/galka/games/Lauctions.pdf · Game Theory Applications: Lecture Notes ... 04.16.01 and 04.18.01 Lecture Notes in Game Theory](https://reader034.vdocuments.us/reader034/viewer/2022052608/5a9e18827f8b9a29228d878f/html5/thumbnails/4.jpg)
04.16.01 and 04.18.01 Lecture Notes in Game Theory 4
Types of Auction Settingsu English Auction
– history: used by major auction houses, Cristie’s and Sotheby’s
– Major Feature: Ascending Priceu Dutch Auction
– history: used in tulip trading– Major Feature: Descending Price
![Page 5: Game Theory Applications: Lecture Notesciti.umich.edu/u/galka/games/Lauctions.pdf · Game Theory Applications: Lecture Notes ... 04.16.01 and 04.18.01 Lecture Notes in Game Theory](https://reader034.vdocuments.us/reader034/viewer/2022052608/5a9e18827f8b9a29228d878f/html5/thumbnails/5.jpg)
04.16.01 and 04.18.01 Lecture Notes in Game Theory 5
Bidding Types– Sealed bid auction
»Advantage: makes collision more difficult
– Open-outcry auction»advantage: casts additional
information to the bidders about the object value
![Page 6: Game Theory Applications: Lecture Notesciti.umich.edu/u/galka/games/Lauctions.pdf · Game Theory Applications: Lecture Notes ... 04.16.01 and 04.18.01 Lecture Notes in Game Theory](https://reader034.vdocuments.us/reader034/viewer/2022052608/5a9e18827f8b9a29228d878f/html5/thumbnails/6.jpg)
04.16.01 and 04.18.01 Lecture Notes in Game Theory 6
Valuation Methodsu Two major methods [types of objects]
– private (subjective valuation)» different bidders value the object differently» example: collectibles
– common (public, objective value)» All bidders have the same value, [but might have
different estimates of this value] » example: oil fields
![Page 7: Game Theory Applications: Lecture Notesciti.umich.edu/u/galka/games/Lauctions.pdf · Game Theory Applications: Lecture Notes ... 04.16.01 and 04.18.01 Lecture Notes in Game Theory](https://reader034.vdocuments.us/reader034/viewer/2022052608/5a9e18827f8b9a29228d878f/html5/thumbnails/7.jpg)
04.16.01 and 04.18.01 Lecture Notes in Game Theory 7
Pricing Schemesu First Price Auction
– no true price revelation – price is shaded (lower than the true
value)u Second Price Auction
– price is revealed truthfully under `reasonable` conditions
– [proven by Vickrey (1996 Nobel Price)]
![Page 8: Game Theory Applications: Lecture Notesciti.umich.edu/u/galka/games/Lauctions.pdf · Game Theory Applications: Lecture Notes ... 04.16.01 and 04.18.01 Lecture Notes in Game Theory](https://reader034.vdocuments.us/reader034/viewer/2022052608/5a9e18827f8b9a29228d878f/html5/thumbnails/8.jpg)
04.16.01 and 04.18.01 Lecture Notes in Game Theory 8
Winner’s Curseu When the Winner’s Curse is a
problem– common value auctions – high level of uncertainty of the object
valueu How to alleviate the Winner’s Curse
– Use Second Price Auction
![Page 9: Game Theory Applications: Lecture Notesciti.umich.edu/u/galka/games/Lauctions.pdf · Game Theory Applications: Lecture Notes ... 04.16.01 and 04.18.01 Lecture Notes in Game Theory](https://reader034.vdocuments.us/reader034/viewer/2022052608/5a9e18827f8b9a29228d878f/html5/thumbnails/9.jpg)
04.16.01 and 04.18.01 Lecture Notes in Game Theory 9
Revenue Equivalence Theoremu `reasonable` conditions are:
– bidders are risk-neutral– object is of a common value– bidder’s estimates of this value are
independent ==>u Revenue Equivalence Theorem holds: All types of auctions on average yield the same outcome (i.e. the same profit [surplus])
![Page 10: Game Theory Applications: Lecture Notesciti.umich.edu/u/galka/games/Lauctions.pdf · Game Theory Applications: Lecture Notes ... 04.16.01 and 04.18.01 Lecture Notes in Game Theory](https://reader034.vdocuments.us/reader034/viewer/2022052608/5a9e18827f8b9a29228d878f/html5/thumbnails/10.jpg)
04.16.01 and 04.18.01 Lecture Notes in Game Theory 10
Departures from the Theorem’s Conditions & Auction Design
u Assume that bidders are risk-averse & object is of a common value & bidder’s estimates of this value are independent – Then
![Page 11: Game Theory Applications: Lecture Notesciti.umich.edu/u/galka/games/Lauctions.pdf · Game Theory Applications: Lecture Notes ... 04.16.01 and 04.18.01 Lecture Notes in Game Theory](https://reader034.vdocuments.us/reader034/viewer/2022052608/5a9e18827f8b9a29228d878f/html5/thumbnails/11.jpg)
04.16.01 and 04.18.01 Lecture Notes in Game Theory 11
Departures from the Theorem’s Conditions & Auction Design
u Assume that bidders are risk-neutral & their valuation estimates are positively correlated– Then
![Page 12: Game Theory Applications: Lecture Notesciti.umich.edu/u/galka/games/Lauctions.pdf · Game Theory Applications: Lecture Notes ... 04.16.01 and 04.18.01 Lecture Notes in Game Theory](https://reader034.vdocuments.us/reader034/viewer/2022052608/5a9e18827f8b9a29228d878f/html5/thumbnails/12.jpg)
04.16.01 and 04.18.01 Lecture Notes in Game Theory 12
All-Pay Auctions u All bidders pay their bids, but only
one [or several] get the object– example: athletic competitions
u Optimal bidding strategy in all-pay auctions:
Use of Mixed strategy
![Page 13: Game Theory Applications: Lecture Notesciti.umich.edu/u/galka/games/Lauctions.pdf · Game Theory Applications: Lecture Notes ... 04.16.01 and 04.18.01 Lecture Notes in Game Theory](https://reader034.vdocuments.us/reader034/viewer/2022052608/5a9e18827f8b9a29228d878f/html5/thumbnails/13.jpg)
04.16.01 and 04.18.01 Lecture Notes in Game Theory 13
Some Other Considerations
u Reserve Price of the objectu Information disclosureu Why e-Bay is a second price auctionu Auctions and Stock market: are
there any similarities?u Auctions and LBOs: are there any
similarities?
![Page 14: Game Theory Applications: Lecture Notesciti.umich.edu/u/galka/games/Lauctions.pdf · Game Theory Applications: Lecture Notes ... 04.16.01 and 04.18.01 Lecture Notes in Game Theory](https://reader034.vdocuments.us/reader034/viewer/2022052608/5a9e18827f8b9a29228d878f/html5/thumbnails/14.jpg)
04.16.01 and 04.18.01 Lecture Notes in Game Theory 14
Government Objective Functionu Duality of Government Objective
– to maximize the auction revenues– to maximize the government revenues that auction
brings [auction revenue & future tax revenues from the corporations who submitted the winning bids]
– to maximize economic efficiency of provision of the goods related to auction in question
– to maximize the total surplus of the specific auction [a sum of government revenues [seller’s surplus], corporate profits [buyer’s or bidder’s surplus], and consumer surplus
![Page 15: Game Theory Applications: Lecture Notesciti.umich.edu/u/galka/games/Lauctions.pdf · Game Theory Applications: Lecture Notes ... 04.16.01 and 04.18.01 Lecture Notes in Game Theory](https://reader034.vdocuments.us/reader034/viewer/2022052608/5a9e18827f8b9a29228d878f/html5/thumbnails/15.jpg)
04.16.01 and 04.18.01 Lecture Notes in Game Theory 15
Can Everyone be a Winner?u Example of California Energy Crisis
– I promise a 6 times drop in the price of electricity in CA [three years ago]
– why the academicians are silent?u Example of British Government
Auction Policy– Klemperer [Oxford] designed the
system for the Government [ seller]– he also consults the companies [bidders]
![Page 16: Game Theory Applications: Lecture Notesciti.umich.edu/u/galka/games/Lauctions.pdf · Game Theory Applications: Lecture Notes ... 04.16.01 and 04.18.01 Lecture Notes in Game Theory](https://reader034.vdocuments.us/reader034/viewer/2022052608/5a9e18827f8b9a29228d878f/html5/thumbnails/16.jpg)
04.16.01 and 04.18.01 Lecture Notes in Game Theory 16
Summary of Auctions Iu auctions can be
» English (ascending) & Dutch (descending)» open outcry & sealed bid» first price & second price» common value & private value
u Auction Theory major results » Revenue Equivalence Theorem» Vickrey’s mechanism (truthful price
revelation via second-price sealed bid auction)
![Page 17: Game Theory Applications: Lecture Notesciti.umich.edu/u/galka/games/Lauctions.pdf · Game Theory Applications: Lecture Notes ... 04.16.01 and 04.18.01 Lecture Notes in Game Theory](https://reader034.vdocuments.us/reader034/viewer/2022052608/5a9e18827f8b9a29228d878f/html5/thumbnails/17.jpg)
04.16.01 and 04.18.01 Lecture Notes in Game Theory 17
Summary of Auctions IIu What matters for auction design
– bidder’s (buyer’s) features:» risk attitude (risk-neutral or risk-averse)» their valuation of the object(independent or
correlated)– Seller’s objective function
» short-term surplus maximization» long -term considerations» economic efficiency (government is a seller)
– Information Structure
![Page 18: Game Theory Applications: Lecture Notesciti.umich.edu/u/galka/games/Lauctions.pdf · Game Theory Applications: Lecture Notes ... 04.16.01 and 04.18.01 Lecture Notes in Game Theory](https://reader034.vdocuments.us/reader034/viewer/2022052608/5a9e18827f8b9a29228d878f/html5/thumbnails/18.jpg)
04.16.01 and 04.18.01 Lecture Notes in Game Theory 18
Summary of the Courseu We learned:
– Dixit, chapters: 1 – 5, 15, 16 + some extras
– Lewis, chapters: ALL (the entire book)u Major Lesson from our studies:
– common sense works– `common` theory works better, because it
» aggregates the common sense, » structures it, and » makes it from the art into a science
![Page 19: Game Theory Applications: Lecture Notesciti.umich.edu/u/galka/games/Lauctions.pdf · Game Theory Applications: Lecture Notes ... 04.16.01 and 04.18.01 Lecture Notes in Game Theory](https://reader034.vdocuments.us/reader034/viewer/2022052608/5a9e18827f8b9a29228d878f/html5/thumbnails/19.jpg)
04.16.01 and 04.18.01 Lecture Notes in Game Theory 1
Game Theory Applications: Lecture Notes
Course Websitehttp://www.citi.umich.edu/u/galka/games
u Galina Albert Schwartzu Department of Financeu University of Michiganu Business School
![Page 20: Game Theory Applications: Lecture Notesciti.umich.edu/u/galka/games/Lauctions.pdf · Game Theory Applications: Lecture Notes ... 04.16.01 and 04.18.01 Lecture Notes in Game Theory](https://reader034.vdocuments.us/reader034/viewer/2022052608/5a9e18827f8b9a29228d878f/html5/thumbnails/20.jpg)
04.16.01 and 04.18.01 Lecture Notes in Game Theory 2
Summary of last two lectures
u Auctions: Dixit, chapter 15u Types of Auctionsu Winner’s Curseu Vickrey’s Theoremu Auction Designu Summary of the Course
![Page 21: Game Theory Applications: Lecture Notesciti.umich.edu/u/galka/games/Lauctions.pdf · Game Theory Applications: Lecture Notes ... 04.16.01 and 04.18.01 Lecture Notes in Game Theory](https://reader034.vdocuments.us/reader034/viewer/2022052608/5a9e18827f8b9a29228d878f/html5/thumbnails/21.jpg)
04.16.01 and 04.18.01 Lecture Notes in Game Theory 3
Auction Design: Types of Auctions
u Four Major Considerations– Types of Auction Settings– Bidding Types– Pricing Schemes– Valuation Methods
![Page 22: Game Theory Applications: Lecture Notesciti.umich.edu/u/galka/games/Lauctions.pdf · Game Theory Applications: Lecture Notes ... 04.16.01 and 04.18.01 Lecture Notes in Game Theory](https://reader034.vdocuments.us/reader034/viewer/2022052608/5a9e18827f8b9a29228d878f/html5/thumbnails/22.jpg)
04.16.01 and 04.18.01 Lecture Notes in Game Theory 4
Types of Auction Settingsu English Auction
– history: used by major auction houses, Cristie’s and Sotheby’s
– Major Feature: Ascending Priceu Dutch Auction
– history: used in tulip trading– Major Feature: Descending Price
![Page 23: Game Theory Applications: Lecture Notesciti.umich.edu/u/galka/games/Lauctions.pdf · Game Theory Applications: Lecture Notes ... 04.16.01 and 04.18.01 Lecture Notes in Game Theory](https://reader034.vdocuments.us/reader034/viewer/2022052608/5a9e18827f8b9a29228d878f/html5/thumbnails/23.jpg)
04.16.01 and 04.18.01 Lecture Notes in Game Theory 5
Bidding Types– Sealed bid auction
»Advantage: makes collision more difficult
– Open-outcry auction»advantage: casts additional
information to the bidders about the object value
![Page 24: Game Theory Applications: Lecture Notesciti.umich.edu/u/galka/games/Lauctions.pdf · Game Theory Applications: Lecture Notes ... 04.16.01 and 04.18.01 Lecture Notes in Game Theory](https://reader034.vdocuments.us/reader034/viewer/2022052608/5a9e18827f8b9a29228d878f/html5/thumbnails/24.jpg)
04.16.01 and 04.18.01 Lecture Notes in Game Theory 6
Valuation Methodsu Two major methods [types of objects]
– private (subjective valuation)» different bidders value the object differently» example: collectibles
– common (public, objective value)» All bidders have the same value, [but might have
different estimates of this value] » example: oil fields
![Page 25: Game Theory Applications: Lecture Notesciti.umich.edu/u/galka/games/Lauctions.pdf · Game Theory Applications: Lecture Notes ... 04.16.01 and 04.18.01 Lecture Notes in Game Theory](https://reader034.vdocuments.us/reader034/viewer/2022052608/5a9e18827f8b9a29228d878f/html5/thumbnails/25.jpg)
04.16.01 and 04.18.01 Lecture Notes in Game Theory 7
Pricing Schemesu First Price Auction
– no true price revelation – price is shaded (lower than the true
value)u Second Price Auction
– price is revealed truthfully under `reasonable` conditions
– [proven by Vickrey (1996 Nobel Price)]
![Page 26: Game Theory Applications: Lecture Notesciti.umich.edu/u/galka/games/Lauctions.pdf · Game Theory Applications: Lecture Notes ... 04.16.01 and 04.18.01 Lecture Notes in Game Theory](https://reader034.vdocuments.us/reader034/viewer/2022052608/5a9e18827f8b9a29228d878f/html5/thumbnails/26.jpg)
04.16.01 and 04.18.01 Lecture Notes in Game Theory 8
Winner’s Curseu When the Winner’s Curse is a
problem– common value auctions – high level of uncertainty of the object
valueu How to alleviate the Winner’s Curse
– Use Second Price Auction
![Page 27: Game Theory Applications: Lecture Notesciti.umich.edu/u/galka/games/Lauctions.pdf · Game Theory Applications: Lecture Notes ... 04.16.01 and 04.18.01 Lecture Notes in Game Theory](https://reader034.vdocuments.us/reader034/viewer/2022052608/5a9e18827f8b9a29228d878f/html5/thumbnails/27.jpg)
04.16.01 and 04.18.01 Lecture Notes in Game Theory 9
Revenue Equivalence Theoremu `reasonable` conditions are:
– bidders are risk-neutral– object is of a common value– bidder’s estimates of this value are
independent ==>u Revenue Equivalence Theorem holds: All types of auctions on average yield the same outcome (i.e. the same profit [surplus])
![Page 28: Game Theory Applications: Lecture Notesciti.umich.edu/u/galka/games/Lauctions.pdf · Game Theory Applications: Lecture Notes ... 04.16.01 and 04.18.01 Lecture Notes in Game Theory](https://reader034.vdocuments.us/reader034/viewer/2022052608/5a9e18827f8b9a29228d878f/html5/thumbnails/28.jpg)
04.16.01 and 04.18.01 Lecture Notes in Game Theory 10
Departures from the Theorem’s Conditions & Auction Design
u Assume that bidders are risk-averse & object is of a common value & bidder’s estimates of this value are independent – Then
![Page 29: Game Theory Applications: Lecture Notesciti.umich.edu/u/galka/games/Lauctions.pdf · Game Theory Applications: Lecture Notes ... 04.16.01 and 04.18.01 Lecture Notes in Game Theory](https://reader034.vdocuments.us/reader034/viewer/2022052608/5a9e18827f8b9a29228d878f/html5/thumbnails/29.jpg)
04.16.01 and 04.18.01 Lecture Notes in Game Theory 11
Departures from the Theorem’s Conditions & Auction Design
u Assume that bidders are risk-neutral & their valuation estimates are positively correlated– Then
![Page 30: Game Theory Applications: Lecture Notesciti.umich.edu/u/galka/games/Lauctions.pdf · Game Theory Applications: Lecture Notes ... 04.16.01 and 04.18.01 Lecture Notes in Game Theory](https://reader034.vdocuments.us/reader034/viewer/2022052608/5a9e18827f8b9a29228d878f/html5/thumbnails/30.jpg)
04.16.01 and 04.18.01 Lecture Notes in Game Theory 12
All-Pay Auctions u All bidders pay their bids, but only
one [or several] get the object– example: athletic competitions
u Optimal bidding strategy in all-pay auctions:
Use of Mixed strategy
![Page 31: Game Theory Applications: Lecture Notesciti.umich.edu/u/galka/games/Lauctions.pdf · Game Theory Applications: Lecture Notes ... 04.16.01 and 04.18.01 Lecture Notes in Game Theory](https://reader034.vdocuments.us/reader034/viewer/2022052608/5a9e18827f8b9a29228d878f/html5/thumbnails/31.jpg)
04.16.01 and 04.18.01 Lecture Notes in Game Theory 13
Some Other Considerations
u Reserve Price of the objectu Information disclosureu Why e-Bay is a second price auctionu Auctions and Stock market: are
there any similarities?u Auctions and LBOs: are there any
similarities?
![Page 32: Game Theory Applications: Lecture Notesciti.umich.edu/u/galka/games/Lauctions.pdf · Game Theory Applications: Lecture Notes ... 04.16.01 and 04.18.01 Lecture Notes in Game Theory](https://reader034.vdocuments.us/reader034/viewer/2022052608/5a9e18827f8b9a29228d878f/html5/thumbnails/32.jpg)
04.16.01 and 04.18.01 Lecture Notes in Game Theory 14
Government Objective Functionu Duality of Government Objective
– to maximize the auction revenues– to maximize the government revenues that auction
brings [auction revenue & future tax revenues from the corporations who submitted the winning bids]
– to maximize economic efficiency of provision of the goods related to auction in question
– to maximize the total surplus of the specific auction [a sum of government revenues [seller’s surplus], corporate profits [buyer’s or bidder’s surplus], and consumer surplus
![Page 33: Game Theory Applications: Lecture Notesciti.umich.edu/u/galka/games/Lauctions.pdf · Game Theory Applications: Lecture Notes ... 04.16.01 and 04.18.01 Lecture Notes in Game Theory](https://reader034.vdocuments.us/reader034/viewer/2022052608/5a9e18827f8b9a29228d878f/html5/thumbnails/33.jpg)
04.16.01 and 04.18.01 Lecture Notes in Game Theory 15
Can Everyone be a Winner?u Example of California Energy Crisis
– I promise a 6 times drop in the price of electricity in CA [three years ago]
– why the academicians are silent?u Example of British Government
Auction Policy– Klemperer [Oxford] designed the
system for the Government [ seller]– he also consults the companies [bidders]
![Page 34: Game Theory Applications: Lecture Notesciti.umich.edu/u/galka/games/Lauctions.pdf · Game Theory Applications: Lecture Notes ... 04.16.01 and 04.18.01 Lecture Notes in Game Theory](https://reader034.vdocuments.us/reader034/viewer/2022052608/5a9e18827f8b9a29228d878f/html5/thumbnails/34.jpg)
04.16.01 and 04.18.01 Lecture Notes in Game Theory 16
Summary of Auctions Iu auctions can be
» English (ascending) & Dutch (descending)» open outcry & sealed bid» first price & second price» common value & private value
u Auction Theory major results » Revenue Equivalence Theorem» Vickrey’s mechanism (truthful price
revelation via second-price sealed bid auction)
![Page 35: Game Theory Applications: Lecture Notesciti.umich.edu/u/galka/games/Lauctions.pdf · Game Theory Applications: Lecture Notes ... 04.16.01 and 04.18.01 Lecture Notes in Game Theory](https://reader034.vdocuments.us/reader034/viewer/2022052608/5a9e18827f8b9a29228d878f/html5/thumbnails/35.jpg)
04.16.01 and 04.18.01 Lecture Notes in Game Theory 17
Summary of Auctions IIu What matters for auction design
– bidder’s (buyer’s) features:» risk attitude (risk-neutral or risk-averse)» their valuation of the object(independent or
correlated)– Seller’s objective function
» short-term surplus maximization» long -term considerations» economic efficiency (government is a seller)
– Information Structure
![Page 36: Game Theory Applications: Lecture Notesciti.umich.edu/u/galka/games/Lauctions.pdf · Game Theory Applications: Lecture Notes ... 04.16.01 and 04.18.01 Lecture Notes in Game Theory](https://reader034.vdocuments.us/reader034/viewer/2022052608/5a9e18827f8b9a29228d878f/html5/thumbnails/36.jpg)
04.16.01 and 04.18.01 Lecture Notes in Game Theory 18
Summary of the Courseu We learned:
– Dixit, chapters: 1 – 5, 15, 16 + some extras
– Lewis, chapters: ALL (the entire book)u Major Lesson from our studies:
– common sense works– `common` theory works better, because it
» aggregates the common sense, » structures it, and » makes it from the art into a science
![Page 37: Game Theory Applications: Lecture Notesciti.umich.edu/u/galka/games/Lauctions.pdf · Game Theory Applications: Lecture Notes ... 04.16.01 and 04.18.01 Lecture Notes in Game Theory](https://reader034.vdocuments.us/reader034/viewer/2022052608/5a9e18827f8b9a29228d878f/html5/thumbnails/37.jpg)
04.16.01 and 04.18.01 Lecture Notes in Game Theory 1
Game Theory Applications: Lecture Notes
Course Websitehttp://www.citi.umich.edu/u/galka/games
u Galina Albert Schwartzu Department of Financeu University of Michiganu Business School
![Page 38: Game Theory Applications: Lecture Notesciti.umich.edu/u/galka/games/Lauctions.pdf · Game Theory Applications: Lecture Notes ... 04.16.01 and 04.18.01 Lecture Notes in Game Theory](https://reader034.vdocuments.us/reader034/viewer/2022052608/5a9e18827f8b9a29228d878f/html5/thumbnails/38.jpg)
04.16.01 and 04.18.01 Lecture Notes in Game Theory 2
Summary of last two lectures
u Auctions: Dixit, chapter 15u Types of Auctionsu Winner’s Curseu Vickrey’s Theoremu Auction Designu Summary of the Course
![Page 39: Game Theory Applications: Lecture Notesciti.umich.edu/u/galka/games/Lauctions.pdf · Game Theory Applications: Lecture Notes ... 04.16.01 and 04.18.01 Lecture Notes in Game Theory](https://reader034.vdocuments.us/reader034/viewer/2022052608/5a9e18827f8b9a29228d878f/html5/thumbnails/39.jpg)
04.16.01 and 04.18.01 Lecture Notes in Game Theory 3
Auction Design: Types of Auctions
u Four Major Considerations– Types of Auction Settings– Bidding Types– Pricing Schemes– Valuation Methods
![Page 40: Game Theory Applications: Lecture Notesciti.umich.edu/u/galka/games/Lauctions.pdf · Game Theory Applications: Lecture Notes ... 04.16.01 and 04.18.01 Lecture Notes in Game Theory](https://reader034.vdocuments.us/reader034/viewer/2022052608/5a9e18827f8b9a29228d878f/html5/thumbnails/40.jpg)
04.16.01 and 04.18.01 Lecture Notes in Game Theory 4
Types of Auction Settingsu English Auction
– history: used by major auction houses, Cristie’s and Sotheby’s
– Major Feature: Ascending Priceu Dutch Auction
– history: used in tulip trading– Major Feature: Descending Price
![Page 41: Game Theory Applications: Lecture Notesciti.umich.edu/u/galka/games/Lauctions.pdf · Game Theory Applications: Lecture Notes ... 04.16.01 and 04.18.01 Lecture Notes in Game Theory](https://reader034.vdocuments.us/reader034/viewer/2022052608/5a9e18827f8b9a29228d878f/html5/thumbnails/41.jpg)
04.16.01 and 04.18.01 Lecture Notes in Game Theory 5
Bidding Types– Sealed bid auction
»Advantage: makes collision more difficult
– Open-outcry auction»advantage: casts additional
information to the bidders about the object value
![Page 42: Game Theory Applications: Lecture Notesciti.umich.edu/u/galka/games/Lauctions.pdf · Game Theory Applications: Lecture Notes ... 04.16.01 and 04.18.01 Lecture Notes in Game Theory](https://reader034.vdocuments.us/reader034/viewer/2022052608/5a9e18827f8b9a29228d878f/html5/thumbnails/42.jpg)
04.16.01 and 04.18.01 Lecture Notes in Game Theory 6
Valuation Methodsu Two major methods [types of objects]
– private (subjective valuation)» different bidders value the object differently» example: collectibles
– common (public, objective value)» All bidders have the same value, [but might have
different estimates of this value] » example: oil fields
![Page 43: Game Theory Applications: Lecture Notesciti.umich.edu/u/galka/games/Lauctions.pdf · Game Theory Applications: Lecture Notes ... 04.16.01 and 04.18.01 Lecture Notes in Game Theory](https://reader034.vdocuments.us/reader034/viewer/2022052608/5a9e18827f8b9a29228d878f/html5/thumbnails/43.jpg)
04.16.01 and 04.18.01 Lecture Notes in Game Theory 7
Pricing Schemesu First Price Auction
– no true price revelation – price is shaded (lower than the true
value)u Second Price Auction
– price is revealed truthfully under `reasonable` conditions
– [proven by Vickrey (1996 Nobel Price)]
![Page 44: Game Theory Applications: Lecture Notesciti.umich.edu/u/galka/games/Lauctions.pdf · Game Theory Applications: Lecture Notes ... 04.16.01 and 04.18.01 Lecture Notes in Game Theory](https://reader034.vdocuments.us/reader034/viewer/2022052608/5a9e18827f8b9a29228d878f/html5/thumbnails/44.jpg)
04.16.01 and 04.18.01 Lecture Notes in Game Theory 8
Winner’s Curseu When the Winner’s Curse is a
problem– common value auctions – high level of uncertainty of the object
valueu How to alleviate the Winner’s Curse
– Use Second Price Auction
![Page 45: Game Theory Applications: Lecture Notesciti.umich.edu/u/galka/games/Lauctions.pdf · Game Theory Applications: Lecture Notes ... 04.16.01 and 04.18.01 Lecture Notes in Game Theory](https://reader034.vdocuments.us/reader034/viewer/2022052608/5a9e18827f8b9a29228d878f/html5/thumbnails/45.jpg)
04.16.01 and 04.18.01 Lecture Notes in Game Theory 9
Revenue Equivalence Theoremu `reasonable` conditions are:
– bidders are risk-neutral– object is of a common value– bidder’s estimates of this value are
independent ==>u Revenue Equivalence Theorem holds: All types of auctions on average yield the same outcome (i.e. the same profit [surplus])
![Page 46: Game Theory Applications: Lecture Notesciti.umich.edu/u/galka/games/Lauctions.pdf · Game Theory Applications: Lecture Notes ... 04.16.01 and 04.18.01 Lecture Notes in Game Theory](https://reader034.vdocuments.us/reader034/viewer/2022052608/5a9e18827f8b9a29228d878f/html5/thumbnails/46.jpg)
04.16.01 and 04.18.01 Lecture Notes in Game Theory 10
Departures from the Theorem’s Conditions & Auction Design
u Assume that bidders are risk-averse & object is of a common value & bidder’s estimates of this value are independent – Then
![Page 47: Game Theory Applications: Lecture Notesciti.umich.edu/u/galka/games/Lauctions.pdf · Game Theory Applications: Lecture Notes ... 04.16.01 and 04.18.01 Lecture Notes in Game Theory](https://reader034.vdocuments.us/reader034/viewer/2022052608/5a9e18827f8b9a29228d878f/html5/thumbnails/47.jpg)
04.16.01 and 04.18.01 Lecture Notes in Game Theory 11
Departures from the Theorem’s Conditions & Auction Design
u Assume that bidders are risk-neutral & their valuation estimates are positively correlated– Then
![Page 48: Game Theory Applications: Lecture Notesciti.umich.edu/u/galka/games/Lauctions.pdf · Game Theory Applications: Lecture Notes ... 04.16.01 and 04.18.01 Lecture Notes in Game Theory](https://reader034.vdocuments.us/reader034/viewer/2022052608/5a9e18827f8b9a29228d878f/html5/thumbnails/48.jpg)
04.16.01 and 04.18.01 Lecture Notes in Game Theory 12
All-Pay Auctions u All bidders pay their bids, but only
one [or several] get the object– example: athletic competitions
u Optimal bidding strategy in all-pay auctions:
Use of Mixed strategy
![Page 49: Game Theory Applications: Lecture Notesciti.umich.edu/u/galka/games/Lauctions.pdf · Game Theory Applications: Lecture Notes ... 04.16.01 and 04.18.01 Lecture Notes in Game Theory](https://reader034.vdocuments.us/reader034/viewer/2022052608/5a9e18827f8b9a29228d878f/html5/thumbnails/49.jpg)
04.16.01 and 04.18.01 Lecture Notes in Game Theory 13
Some Other Considerations
u Reserve Price of the objectu Information disclosureu Why e-Bay is a second price auctionu Auctions and Stock market: are
there any similarities?u Auctions and LBOs: are there any
similarities?
![Page 50: Game Theory Applications: Lecture Notesciti.umich.edu/u/galka/games/Lauctions.pdf · Game Theory Applications: Lecture Notes ... 04.16.01 and 04.18.01 Lecture Notes in Game Theory](https://reader034.vdocuments.us/reader034/viewer/2022052608/5a9e18827f8b9a29228d878f/html5/thumbnails/50.jpg)
04.16.01 and 04.18.01 Lecture Notes in Game Theory 14
Government Objective Functionu Duality of Government Objective
– to maximize the auction revenues– to maximize the government revenues that auction
brings [auction revenue & future tax revenues from the corporations who submitted the winning bids]
– to maximize economic efficiency of provision of the goods related to auction in question
– to maximize the total surplus of the specific auction [a sum of government revenues [seller’s surplus], corporate profits [buyer’s or bidder’s surplus], and consumer surplus
![Page 51: Game Theory Applications: Lecture Notesciti.umich.edu/u/galka/games/Lauctions.pdf · Game Theory Applications: Lecture Notes ... 04.16.01 and 04.18.01 Lecture Notes in Game Theory](https://reader034.vdocuments.us/reader034/viewer/2022052608/5a9e18827f8b9a29228d878f/html5/thumbnails/51.jpg)
04.16.01 and 04.18.01 Lecture Notes in Game Theory 15
Can Everyone be a Winner?u Example of California Energy Crisis
– I promise a 6 times drop in the price of electricity in CA [three years ago]
– why the academicians are silent?u Example of British Government
Auction Policy– Klemperer [Oxford] designed the
system for the Government [ seller]– he also consults the companies [bidders]
![Page 52: Game Theory Applications: Lecture Notesciti.umich.edu/u/galka/games/Lauctions.pdf · Game Theory Applications: Lecture Notes ... 04.16.01 and 04.18.01 Lecture Notes in Game Theory](https://reader034.vdocuments.us/reader034/viewer/2022052608/5a9e18827f8b9a29228d878f/html5/thumbnails/52.jpg)
04.16.01 and 04.18.01 Lecture Notes in Game Theory 16
Summary of Auctions Iu auctions can be
» English (ascending) & Dutch (descending)» open outcry & sealed bid» first price & second price» common value & private value
u Auction Theory major results » Revenue Equivalence Theorem» Vickrey’s mechanism (truthful price
revelation via second-price sealed bid auction)
![Page 53: Game Theory Applications: Lecture Notesciti.umich.edu/u/galka/games/Lauctions.pdf · Game Theory Applications: Lecture Notes ... 04.16.01 and 04.18.01 Lecture Notes in Game Theory](https://reader034.vdocuments.us/reader034/viewer/2022052608/5a9e18827f8b9a29228d878f/html5/thumbnails/53.jpg)
04.16.01 and 04.18.01 Lecture Notes in Game Theory 17
Summary of Auctions IIu What matters for auction design
– bidder’s (buyer’s) features:» risk attitude (risk-neutral or risk-averse)» their valuation of the object(independent or
correlated)– Seller’s objective function
» short-term surplus maximization» long -term considerations» economic efficiency (government is a seller)
– Information Structure
![Page 54: Game Theory Applications: Lecture Notesciti.umich.edu/u/galka/games/Lauctions.pdf · Game Theory Applications: Lecture Notes ... 04.16.01 and 04.18.01 Lecture Notes in Game Theory](https://reader034.vdocuments.us/reader034/viewer/2022052608/5a9e18827f8b9a29228d878f/html5/thumbnails/54.jpg)
04.16.01 and 04.18.01 Lecture Notes in Game Theory 18
Summary of the Courseu We learned:
– Dixit, chapters: 1 – 5, 15, 16 + some extras
– Lewis, chapters: ALL (the entire book)u Major Lesson from our studies:
– common sense works– `common` theory works better, because it
» aggregates the common sense, » structures it, and » makes it from the art into a science
![Page 55: Game Theory Applications: Lecture Notesciti.umich.edu/u/galka/games/Lauctions.pdf · Game Theory Applications: Lecture Notes ... 04.16.01 and 04.18.01 Lecture Notes in Game Theory](https://reader034.vdocuments.us/reader034/viewer/2022052608/5a9e18827f8b9a29228d878f/html5/thumbnails/55.jpg)
04.16.01 and 04.18.01 Lecture Notes in Game Theory 1
Game Theory Applications: Lecture Notes
Course Websitehttp://www.citi.umich.edu/u/galka/games
u Galina Albert Schwartzu Department of Financeu University of Michiganu Business School
![Page 56: Game Theory Applications: Lecture Notesciti.umich.edu/u/galka/games/Lauctions.pdf · Game Theory Applications: Lecture Notes ... 04.16.01 and 04.18.01 Lecture Notes in Game Theory](https://reader034.vdocuments.us/reader034/viewer/2022052608/5a9e18827f8b9a29228d878f/html5/thumbnails/56.jpg)
04.16.01 and 04.18.01 Lecture Notes in Game Theory 2
Summary of last two lectures
u Auctions: Dixit, chapter 15u Types of Auctionsu Winner’s Curseu Vickrey’s Theoremu Auction Designu Summary of the Course
![Page 57: Game Theory Applications: Lecture Notesciti.umich.edu/u/galka/games/Lauctions.pdf · Game Theory Applications: Lecture Notes ... 04.16.01 and 04.18.01 Lecture Notes in Game Theory](https://reader034.vdocuments.us/reader034/viewer/2022052608/5a9e18827f8b9a29228d878f/html5/thumbnails/57.jpg)
04.16.01 and 04.18.01 Lecture Notes in Game Theory 3
Auction Design: Types of Auctions
u Four Major Considerations– Types of Auction Settings– Bidding Types– Pricing Schemes– Valuation Methods
![Page 58: Game Theory Applications: Lecture Notesciti.umich.edu/u/galka/games/Lauctions.pdf · Game Theory Applications: Lecture Notes ... 04.16.01 and 04.18.01 Lecture Notes in Game Theory](https://reader034.vdocuments.us/reader034/viewer/2022052608/5a9e18827f8b9a29228d878f/html5/thumbnails/58.jpg)
04.16.01 and 04.18.01 Lecture Notes in Game Theory 4
Types of Auction Settingsu English Auction
– history: used by major auction houses, Cristie’s and Sotheby’s
– Major Feature: Ascending Priceu Dutch Auction
– history: used in tulip trading– Major Feature: Descending Price
![Page 59: Game Theory Applications: Lecture Notesciti.umich.edu/u/galka/games/Lauctions.pdf · Game Theory Applications: Lecture Notes ... 04.16.01 and 04.18.01 Lecture Notes in Game Theory](https://reader034.vdocuments.us/reader034/viewer/2022052608/5a9e18827f8b9a29228d878f/html5/thumbnails/59.jpg)
04.16.01 and 04.18.01 Lecture Notes in Game Theory 5
Bidding Types– Sealed bid auction
»Advantage: makes collision more difficult
– Open-outcry auction»advantage: casts additional
information to the bidders about the object value
![Page 60: Game Theory Applications: Lecture Notesciti.umich.edu/u/galka/games/Lauctions.pdf · Game Theory Applications: Lecture Notes ... 04.16.01 and 04.18.01 Lecture Notes in Game Theory](https://reader034.vdocuments.us/reader034/viewer/2022052608/5a9e18827f8b9a29228d878f/html5/thumbnails/60.jpg)
04.16.01 and 04.18.01 Lecture Notes in Game Theory 6
Valuation Methodsu Two major methods [types of objects]
– private (subjective valuation)» different bidders value the object differently» example: collectibles
– common (public, objective value)» All bidders have the same value, [but might have
different estimates of this value] » example: oil fields
![Page 61: Game Theory Applications: Lecture Notesciti.umich.edu/u/galka/games/Lauctions.pdf · Game Theory Applications: Lecture Notes ... 04.16.01 and 04.18.01 Lecture Notes in Game Theory](https://reader034.vdocuments.us/reader034/viewer/2022052608/5a9e18827f8b9a29228d878f/html5/thumbnails/61.jpg)
04.16.01 and 04.18.01 Lecture Notes in Game Theory 7
Pricing Schemesu First Price Auction
– no true price revelation – price is shaded (lower than the true
value)u Second Price Auction
– price is revealed truthfully under `reasonable` conditions
– [proven by Vickrey (1996 Nobel Price)]
![Page 62: Game Theory Applications: Lecture Notesciti.umich.edu/u/galka/games/Lauctions.pdf · Game Theory Applications: Lecture Notes ... 04.16.01 and 04.18.01 Lecture Notes in Game Theory](https://reader034.vdocuments.us/reader034/viewer/2022052608/5a9e18827f8b9a29228d878f/html5/thumbnails/62.jpg)
04.16.01 and 04.18.01 Lecture Notes in Game Theory 8
Winner’s Curseu When the Winner’s Curse is a
problem– common value auctions – high level of uncertainty of the object
valueu How to alleviate the Winner’s Curse
– Use Second Price Auction
![Page 63: Game Theory Applications: Lecture Notesciti.umich.edu/u/galka/games/Lauctions.pdf · Game Theory Applications: Lecture Notes ... 04.16.01 and 04.18.01 Lecture Notes in Game Theory](https://reader034.vdocuments.us/reader034/viewer/2022052608/5a9e18827f8b9a29228d878f/html5/thumbnails/63.jpg)
04.16.01 and 04.18.01 Lecture Notes in Game Theory 9
Revenue Equivalence Theoremu `reasonable` conditions are:
– bidders are risk-neutral– object is of a common value– bidder’s estimates of this value are
independent ==>u Revenue Equivalence Theorem holds: All types of auctions on average yield the same outcome (i.e. the same profit [surplus])
![Page 64: Game Theory Applications: Lecture Notesciti.umich.edu/u/galka/games/Lauctions.pdf · Game Theory Applications: Lecture Notes ... 04.16.01 and 04.18.01 Lecture Notes in Game Theory](https://reader034.vdocuments.us/reader034/viewer/2022052608/5a9e18827f8b9a29228d878f/html5/thumbnails/64.jpg)
04.16.01 and 04.18.01 Lecture Notes in Game Theory 10
Departures from the Theorem’s Conditions & Auction Design
u Assume that bidders are risk-averse & object is of a common value & bidder’s estimates of this value are independent – Then
![Page 65: Game Theory Applications: Lecture Notesciti.umich.edu/u/galka/games/Lauctions.pdf · Game Theory Applications: Lecture Notes ... 04.16.01 and 04.18.01 Lecture Notes in Game Theory](https://reader034.vdocuments.us/reader034/viewer/2022052608/5a9e18827f8b9a29228d878f/html5/thumbnails/65.jpg)
04.16.01 and 04.18.01 Lecture Notes in Game Theory 11
Departures from the Theorem’s Conditions & Auction Design
u Assume that bidders are risk-neutral & their valuation estimates are positively correlated– Then
![Page 66: Game Theory Applications: Lecture Notesciti.umich.edu/u/galka/games/Lauctions.pdf · Game Theory Applications: Lecture Notes ... 04.16.01 and 04.18.01 Lecture Notes in Game Theory](https://reader034.vdocuments.us/reader034/viewer/2022052608/5a9e18827f8b9a29228d878f/html5/thumbnails/66.jpg)
04.16.01 and 04.18.01 Lecture Notes in Game Theory 12
All-Pay Auctions u All bidders pay their bids, but only
one [or several] get the object– example: athletic competitions
u Optimal bidding strategy in all-pay auctions:
Use of Mixed strategy
![Page 67: Game Theory Applications: Lecture Notesciti.umich.edu/u/galka/games/Lauctions.pdf · Game Theory Applications: Lecture Notes ... 04.16.01 and 04.18.01 Lecture Notes in Game Theory](https://reader034.vdocuments.us/reader034/viewer/2022052608/5a9e18827f8b9a29228d878f/html5/thumbnails/67.jpg)
04.16.01 and 04.18.01 Lecture Notes in Game Theory 13
Some Other Considerations
u Reserve Price of the objectu Information disclosureu Why e-Bay is a second price auctionu Auctions and Stock market: are
there any similarities?u Auctions and LBOs: are there any
similarities?
![Page 68: Game Theory Applications: Lecture Notesciti.umich.edu/u/galka/games/Lauctions.pdf · Game Theory Applications: Lecture Notes ... 04.16.01 and 04.18.01 Lecture Notes in Game Theory](https://reader034.vdocuments.us/reader034/viewer/2022052608/5a9e18827f8b9a29228d878f/html5/thumbnails/68.jpg)
04.16.01 and 04.18.01 Lecture Notes in Game Theory 14
Government Objective Functionu Duality of Government Objective
– to maximize the auction revenues– to maximize the government revenues that auction
brings [auction revenue & future tax revenues from the corporations who submitted the winning bids]
– to maximize economic efficiency of provision of the goods related to auction in question
– to maximize the total surplus of the specific auction [a sum of government revenues [seller’s surplus], corporate profits [buyer’s or bidder’s surplus], and consumer surplus
![Page 69: Game Theory Applications: Lecture Notesciti.umich.edu/u/galka/games/Lauctions.pdf · Game Theory Applications: Lecture Notes ... 04.16.01 and 04.18.01 Lecture Notes in Game Theory](https://reader034.vdocuments.us/reader034/viewer/2022052608/5a9e18827f8b9a29228d878f/html5/thumbnails/69.jpg)
04.16.01 and 04.18.01 Lecture Notes in Game Theory 15
Can Everyone be a Winner?u Example of California Energy Crisis
– I promise a 6 times drop in the price of electricity in CA [three years ago]
– why the academicians are silent?u Example of British Government
Auction Policy– Klemperer [Oxford] designed the
system for the Government [ seller]– he also consults the companies [bidders]
![Page 70: Game Theory Applications: Lecture Notesciti.umich.edu/u/galka/games/Lauctions.pdf · Game Theory Applications: Lecture Notes ... 04.16.01 and 04.18.01 Lecture Notes in Game Theory](https://reader034.vdocuments.us/reader034/viewer/2022052608/5a9e18827f8b9a29228d878f/html5/thumbnails/70.jpg)
04.16.01 and 04.18.01 Lecture Notes in Game Theory 16
Summary of Auctions Iu auctions can be
» English (ascending) & Dutch (descending)» open outcry & sealed bid» first price & second price» common value & private value
u Auction Theory major results » Revenue Equivalence Theorem» Vickrey’s mechanism (truthful price
revelation via second-price sealed bid auction)
![Page 71: Game Theory Applications: Lecture Notesciti.umich.edu/u/galka/games/Lauctions.pdf · Game Theory Applications: Lecture Notes ... 04.16.01 and 04.18.01 Lecture Notes in Game Theory](https://reader034.vdocuments.us/reader034/viewer/2022052608/5a9e18827f8b9a29228d878f/html5/thumbnails/71.jpg)
04.16.01 and 04.18.01 Lecture Notes in Game Theory 17
Summary of Auctions IIu What matters for auction design
– bidder’s (buyer’s) features:» risk attitude (risk-neutral or risk-averse)» their valuation of the object(independent or
correlated)– Seller’s objective function
» short-term surplus maximization» long -term considerations» economic efficiency (government is a seller)
– Information Structure
![Page 72: Game Theory Applications: Lecture Notesciti.umich.edu/u/galka/games/Lauctions.pdf · Game Theory Applications: Lecture Notes ... 04.16.01 and 04.18.01 Lecture Notes in Game Theory](https://reader034.vdocuments.us/reader034/viewer/2022052608/5a9e18827f8b9a29228d878f/html5/thumbnails/72.jpg)
04.16.01 and 04.18.01 Lecture Notes in Game Theory 18
Summary of the Courseu We learned:
– Dixit, chapters: 1 – 5, 15, 16 + some extras
– Lewis, chapters: ALL (the entire book)u Major Lesson from our studies:
– common sense works– `common` theory works better, because it
» aggregates the common sense, » structures it, and » makes it from the art into a science
![Page 73: Game Theory Applications: Lecture Notesciti.umich.edu/u/galka/games/Lauctions.pdf · Game Theory Applications: Lecture Notes ... 04.16.01 and 04.18.01 Lecture Notes in Game Theory](https://reader034.vdocuments.us/reader034/viewer/2022052608/5a9e18827f8b9a29228d878f/html5/thumbnails/73.jpg)
04.16.01 and 04.18.01 Lecture Notes in Game Theory 1
Game Theory Applications: Lecture Notes
Course Websitehttp://www.citi.umich.edu/u/galka/games
u Galina Albert Schwartzu Department of Financeu University of Michiganu Business School
![Page 74: Game Theory Applications: Lecture Notesciti.umich.edu/u/galka/games/Lauctions.pdf · Game Theory Applications: Lecture Notes ... 04.16.01 and 04.18.01 Lecture Notes in Game Theory](https://reader034.vdocuments.us/reader034/viewer/2022052608/5a9e18827f8b9a29228d878f/html5/thumbnails/74.jpg)
04.16.01 and 04.18.01 Lecture Notes in Game Theory 2
Summary of last two lectures
u Auctions: Dixit, chapter 15u Types of Auctionsu Winner’s Curseu Vickrey’s Theoremu Auction Designu Summary of the Course
![Page 75: Game Theory Applications: Lecture Notesciti.umich.edu/u/galka/games/Lauctions.pdf · Game Theory Applications: Lecture Notes ... 04.16.01 and 04.18.01 Lecture Notes in Game Theory](https://reader034.vdocuments.us/reader034/viewer/2022052608/5a9e18827f8b9a29228d878f/html5/thumbnails/75.jpg)
04.16.01 and 04.18.01 Lecture Notes in Game Theory 3
Auction Design: Types of Auctions
u Four Major Considerations– Types of Auction Settings– Bidding Types– Pricing Schemes– Valuation Methods
![Page 76: Game Theory Applications: Lecture Notesciti.umich.edu/u/galka/games/Lauctions.pdf · Game Theory Applications: Lecture Notes ... 04.16.01 and 04.18.01 Lecture Notes in Game Theory](https://reader034.vdocuments.us/reader034/viewer/2022052608/5a9e18827f8b9a29228d878f/html5/thumbnails/76.jpg)
04.16.01 and 04.18.01 Lecture Notes in Game Theory 4
Types of Auction Settingsu English Auction
– history: used by major auction houses, Cristie’s and Sotheby’s
– Major Feature: Ascending Priceu Dutch Auction
– history: used in tulip trading– Major Feature: Descending Price
![Page 77: Game Theory Applications: Lecture Notesciti.umich.edu/u/galka/games/Lauctions.pdf · Game Theory Applications: Lecture Notes ... 04.16.01 and 04.18.01 Lecture Notes in Game Theory](https://reader034.vdocuments.us/reader034/viewer/2022052608/5a9e18827f8b9a29228d878f/html5/thumbnails/77.jpg)
04.16.01 and 04.18.01 Lecture Notes in Game Theory 5
Bidding Types– Sealed bid auction
»Advantage: makes collision more difficult
– Open-outcry auction»advantage: casts additional
information to the bidders about the object value
![Page 78: Game Theory Applications: Lecture Notesciti.umich.edu/u/galka/games/Lauctions.pdf · Game Theory Applications: Lecture Notes ... 04.16.01 and 04.18.01 Lecture Notes in Game Theory](https://reader034.vdocuments.us/reader034/viewer/2022052608/5a9e18827f8b9a29228d878f/html5/thumbnails/78.jpg)
04.16.01 and 04.18.01 Lecture Notes in Game Theory 6
Valuation Methodsu Two major methods [types of objects]
– private (subjective valuation)» different bidders value the object differently» example: collectibles
– common (public, objective value)» All bidders have the same value, [but might have
different estimates of this value] » example: oil fields
![Page 79: Game Theory Applications: Lecture Notesciti.umich.edu/u/galka/games/Lauctions.pdf · Game Theory Applications: Lecture Notes ... 04.16.01 and 04.18.01 Lecture Notes in Game Theory](https://reader034.vdocuments.us/reader034/viewer/2022052608/5a9e18827f8b9a29228d878f/html5/thumbnails/79.jpg)
04.16.01 and 04.18.01 Lecture Notes in Game Theory 7
Pricing Schemesu First Price Auction
– no true price revelation – price is shaded (lower than the true
value)u Second Price Auction
– price is revealed truthfully under `reasonable` conditions
– [proven by Vickrey (1996 Nobel Price)]
![Page 80: Game Theory Applications: Lecture Notesciti.umich.edu/u/galka/games/Lauctions.pdf · Game Theory Applications: Lecture Notes ... 04.16.01 and 04.18.01 Lecture Notes in Game Theory](https://reader034.vdocuments.us/reader034/viewer/2022052608/5a9e18827f8b9a29228d878f/html5/thumbnails/80.jpg)
04.16.01 and 04.18.01 Lecture Notes in Game Theory 8
Winner’s Curseu When the Winner’s Curse is a
problem– common value auctions – high level of uncertainty of the object
valueu How to alleviate the Winner’s Curse
– Use Second Price Auction
![Page 81: Game Theory Applications: Lecture Notesciti.umich.edu/u/galka/games/Lauctions.pdf · Game Theory Applications: Lecture Notes ... 04.16.01 and 04.18.01 Lecture Notes in Game Theory](https://reader034.vdocuments.us/reader034/viewer/2022052608/5a9e18827f8b9a29228d878f/html5/thumbnails/81.jpg)
04.16.01 and 04.18.01 Lecture Notes in Game Theory 9
Revenue Equivalence Theoremu `reasonable` conditions are:
– bidders are risk-neutral– object is of a common value– bidder’s estimates of this value are
independent ==>u Revenue Equivalence Theorem holds: All types of auctions on average yield the same outcome (i.e. the same profit [surplus])
![Page 82: Game Theory Applications: Lecture Notesciti.umich.edu/u/galka/games/Lauctions.pdf · Game Theory Applications: Lecture Notes ... 04.16.01 and 04.18.01 Lecture Notes in Game Theory](https://reader034.vdocuments.us/reader034/viewer/2022052608/5a9e18827f8b9a29228d878f/html5/thumbnails/82.jpg)
04.16.01 and 04.18.01 Lecture Notes in Game Theory 10
Departures from the Theorem’s Conditions & Auction Design
u Assume that bidders are risk-averse & object is of a common value & bidder’s estimates of this value are independent – Then
![Page 83: Game Theory Applications: Lecture Notesciti.umich.edu/u/galka/games/Lauctions.pdf · Game Theory Applications: Lecture Notes ... 04.16.01 and 04.18.01 Lecture Notes in Game Theory](https://reader034.vdocuments.us/reader034/viewer/2022052608/5a9e18827f8b9a29228d878f/html5/thumbnails/83.jpg)
04.16.01 and 04.18.01 Lecture Notes in Game Theory 11
Departures from the Theorem’s Conditions & Auction Design
u Assume that bidders are risk-neutral & their valuation estimates are positively correlated– Then
![Page 84: Game Theory Applications: Lecture Notesciti.umich.edu/u/galka/games/Lauctions.pdf · Game Theory Applications: Lecture Notes ... 04.16.01 and 04.18.01 Lecture Notes in Game Theory](https://reader034.vdocuments.us/reader034/viewer/2022052608/5a9e18827f8b9a29228d878f/html5/thumbnails/84.jpg)
04.16.01 and 04.18.01 Lecture Notes in Game Theory 12
All-Pay Auctions u All bidders pay their bids, but only
one [or several] get the object– example: athletic competitions
u Optimal bidding strategy in all-pay auctions:
Use of Mixed strategy
![Page 85: Game Theory Applications: Lecture Notesciti.umich.edu/u/galka/games/Lauctions.pdf · Game Theory Applications: Lecture Notes ... 04.16.01 and 04.18.01 Lecture Notes in Game Theory](https://reader034.vdocuments.us/reader034/viewer/2022052608/5a9e18827f8b9a29228d878f/html5/thumbnails/85.jpg)
04.16.01 and 04.18.01 Lecture Notes in Game Theory 13
Some Other Considerations
u Reserve Price of the objectu Information disclosureu Why e-Bay is a second price auctionu Auctions and Stock market: are
there any similarities?u Auctions and LBOs: are there any
similarities?
![Page 86: Game Theory Applications: Lecture Notesciti.umich.edu/u/galka/games/Lauctions.pdf · Game Theory Applications: Lecture Notes ... 04.16.01 and 04.18.01 Lecture Notes in Game Theory](https://reader034.vdocuments.us/reader034/viewer/2022052608/5a9e18827f8b9a29228d878f/html5/thumbnails/86.jpg)
04.16.01 and 04.18.01 Lecture Notes in Game Theory 14
Government Objective Functionu Duality of Government Objective
– to maximize the auction revenues– to maximize the government revenues that auction
brings [auction revenue & future tax revenues from the corporations who submitted the winning bids]
– to maximize economic efficiency of provision of the goods related to auction in question
– to maximize the total surplus of the specific auction [a sum of government revenues [seller’s surplus], corporate profits [buyer’s or bidder’s surplus], and consumer surplus
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04.16.01 and 04.18.01 Lecture Notes in Game Theory 15
Can Everyone be a Winner?u Example of California Energy Crisis
– I promise a 6 times drop in the price of electricity in CA [three years ago]
– why the academicians are silent?u Example of British Government
Auction Policy– Klemperer [Oxford] designed the
system for the Government [ seller]– he also consults the companies [bidders]
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04.16.01 and 04.18.01 Lecture Notes in Game Theory 16
Summary of Auctions Iu auctions can be
» English (ascending) & Dutch (descending)» open outcry & sealed bid» first price & second price» common value & private value
u Auction Theory major results » Revenue Equivalence Theorem» Vickrey’s mechanism (truthful price
revelation via second-price sealed bid auction)
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04.16.01 and 04.18.01 Lecture Notes in Game Theory 17
Summary of Auctions IIu What matters for auction design
– bidder’s (buyer’s) features:» risk attitude (risk-neutral or risk-averse)» their valuation of the object(independent or
correlated)– Seller’s objective function
» short-term surplus maximization» long -term considerations» economic efficiency (government is a seller)
– Information Structure
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04.16.01 and 04.18.01 Lecture Notes in Game Theory 18
Summary of the Courseu We learned:
– Dixit, chapters: 1 – 5, 15, 16 + some extras
– Lewis, chapters: ALL (the entire book)u Major Lesson from our studies:
– common sense works– `common` theory works better, because it
» aggregates the common sense, » structures it, and » makes it from the art into a science
![Page 91: Game Theory Applications: Lecture Notesciti.umich.edu/u/galka/games/Lauctions.pdf · Game Theory Applications: Lecture Notes ... 04.16.01 and 04.18.01 Lecture Notes in Game Theory](https://reader034.vdocuments.us/reader034/viewer/2022052608/5a9e18827f8b9a29228d878f/html5/thumbnails/91.jpg)
04.16.01 and 04.18.01 Lecture Notes in Game Theory 1
Game Theory Applications: Lecture Notes
Course Websitehttp://www.citi.umich.edu/u/galka/games
u Galina Albert Schwartzu Department of Financeu University of Michiganu Business School
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04.16.01 and 04.18.01 Lecture Notes in Game Theory 2
Summary of last two lectures
u Auctions: Dixit, chapter 15u Types of Auctionsu Winner’s Curseu Vickrey’s Theoremu Auction Designu Summary of the Course
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04.16.01 and 04.18.01 Lecture Notes in Game Theory 3
Auction Design: Types of Auctions
u Four Major Considerations– Types of Auction Settings– Bidding Types– Pricing Schemes– Valuation Methods
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04.16.01 and 04.18.01 Lecture Notes in Game Theory 4
Types of Auction Settingsu English Auction
– history: used by major auction houses, Cristie’s and Sotheby’s
– Major Feature: Ascending Priceu Dutch Auction
– history: used in tulip trading– Major Feature: Descending Price
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04.16.01 and 04.18.01 Lecture Notes in Game Theory 5
Bidding Types– Sealed bid auction
»Advantage: makes collision more difficult
– Open-outcry auction»advantage: casts additional
information to the bidders about the object value
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04.16.01 and 04.18.01 Lecture Notes in Game Theory 6
Valuation Methodsu Two major methods [types of objects]
– private (subjective valuation)» different bidders value the object differently» example: collectibles
– common (public, objective value)» All bidders have the same value, [but might have
different estimates of this value] » example: oil fields
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04.16.01 and 04.18.01 Lecture Notes in Game Theory 7
Pricing Schemesu First Price Auction
– no true price revelation – price is shaded (lower than the true
value)u Second Price Auction
– price is revealed truthfully under `reasonable` conditions
– [proven by Vickrey (1996 Nobel Price)]
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04.16.01 and 04.18.01 Lecture Notes in Game Theory 8
Winner’s Curseu When the Winner’s Curse is a
problem– common value auctions – high level of uncertainty of the object
valueu How to alleviate the Winner’s Curse
– Use Second Price Auction
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04.16.01 and 04.18.01 Lecture Notes in Game Theory 9
Revenue Equivalence Theoremu `reasonable` conditions are:
– bidders are risk-neutral– object is of a common value– bidder’s estimates of this value are
independent ==>u Revenue Equivalence Theorem holds: All types of auctions on average yield the same outcome (i.e. the same profit [surplus])
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04.16.01 and 04.18.01 Lecture Notes in Game Theory 10
Departures from the Theorem’s Conditions & Auction Design
u Assume that bidders are risk-averse & object is of a common value & bidder’s estimates of this value are independent – Then
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04.16.01 and 04.18.01 Lecture Notes in Game Theory 11
Departures from the Theorem’s Conditions & Auction Design
u Assume that bidders are risk-neutral & their valuation estimates are positively correlated– Then
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04.16.01 and 04.18.01 Lecture Notes in Game Theory 12
All-Pay Auctions u All bidders pay their bids, but only
one [or several] get the object– example: athletic competitions
u Optimal bidding strategy in all-pay auctions:
Use of Mixed strategy
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04.16.01 and 04.18.01 Lecture Notes in Game Theory 13
Some Other Considerations
u Reserve Price of the objectu Information disclosureu Why e-Bay is a second price auctionu Auctions and Stock market: are
there any similarities?u Auctions and LBOs: are there any
similarities?
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04.16.01 and 04.18.01 Lecture Notes in Game Theory 14
Government Objective Functionu Duality of Government Objective
– to maximize the auction revenues– to maximize the government revenues that auction
brings [auction revenue & future tax revenues from the corporations who submitted the winning bids]
– to maximize economic efficiency of provision of the goods related to auction in question
– to maximize the total surplus of the specific auction [a sum of government revenues [seller’s surplus], corporate profits [buyer’s or bidder’s surplus], and consumer surplus
![Page 105: Game Theory Applications: Lecture Notesciti.umich.edu/u/galka/games/Lauctions.pdf · Game Theory Applications: Lecture Notes ... 04.16.01 and 04.18.01 Lecture Notes in Game Theory](https://reader034.vdocuments.us/reader034/viewer/2022052608/5a9e18827f8b9a29228d878f/html5/thumbnails/105.jpg)
04.16.01 and 04.18.01 Lecture Notes in Game Theory 15
Can Everyone be a Winner?u Example of California Energy Crisis
– I promise a 6 times drop in the price of electricity in CA [three years ago]
– why the academicians are silent?u Example of British Government
Auction Policy– Klemperer [Oxford] designed the
system for the Government [ seller]– he also consults the companies [bidders]
![Page 106: Game Theory Applications: Lecture Notesciti.umich.edu/u/galka/games/Lauctions.pdf · Game Theory Applications: Lecture Notes ... 04.16.01 and 04.18.01 Lecture Notes in Game Theory](https://reader034.vdocuments.us/reader034/viewer/2022052608/5a9e18827f8b9a29228d878f/html5/thumbnails/106.jpg)
04.16.01 and 04.18.01 Lecture Notes in Game Theory 16
Summary of Auctions Iu auctions can be
» English (ascending) & Dutch (descending)» open outcry & sealed bid» first price & second price» common value & private value
u Auction Theory major results » Revenue Equivalence Theorem» Vickrey’s mechanism (truthful price
revelation via second-price sealed bid auction)
![Page 107: Game Theory Applications: Lecture Notesciti.umich.edu/u/galka/games/Lauctions.pdf · Game Theory Applications: Lecture Notes ... 04.16.01 and 04.18.01 Lecture Notes in Game Theory](https://reader034.vdocuments.us/reader034/viewer/2022052608/5a9e18827f8b9a29228d878f/html5/thumbnails/107.jpg)
04.16.01 and 04.18.01 Lecture Notes in Game Theory 17
Summary of Auctions IIu What matters for auction design
– bidder’s (buyer’s) features:» risk attitude (risk-neutral or risk-averse)» their valuation of the object(independent or
correlated)– Seller’s objective function
» short-term surplus maximization» long -term considerations» economic efficiency (government is a seller)
– Information Structure
![Page 108: Game Theory Applications: Lecture Notesciti.umich.edu/u/galka/games/Lauctions.pdf · Game Theory Applications: Lecture Notes ... 04.16.01 and 04.18.01 Lecture Notes in Game Theory](https://reader034.vdocuments.us/reader034/viewer/2022052608/5a9e18827f8b9a29228d878f/html5/thumbnails/108.jpg)
04.16.01 and 04.18.01 Lecture Notes in Game Theory 18
Summary of the Courseu We learned:
– Dixit, chapters: 1 – 5, 15, 16 + some extras
– Lewis, chapters: ALL (the entire book)u Major Lesson from our studies:
– common sense works– `common` theory works better, because it
» aggregates the common sense, » structures it, and » makes it from the art into a science