# Introduction to Auction Design

Size: px
Start display at page:

## Transcription

2 tion function describes agent i s intrinsic preference for each outcome. An agent s valuation function is known only to that agent. T denotes the set of all possible valuation functions and v T n is the vector of valuation functions of all agents. The mechanism works by asking each agent to report her valuation function and computing an outcome and a set of payments based on the reported functions. b i denotes the valuation function reported by agent i (also known as i s bid), b T n denotes the vector of bids. P i : T n R be the payment made by agent i, and P = (P i ) i N be the payment scheme. Thus, a mechanism M consists of a pair (O, P ), where O : T n O is the output function and P is the payment scheme. Each agent s goal is to maximize her utility function, which is assumed to be of the form u i (O, P i ) = v i (O) P i Since the mechanism determines the outcome and the payments based on the bid vector b, we will abbreviate u i (O(b), P i (b)) and v i (O(b)) to u i (b) and v i (b) respectively. Clearly, an agent s utility depends not only on her valuation function, but also on the bid vector. Let b i = (b 1,..., b i 1,?, b i+1,... b n ) denote the vector of bids with agent i s bid hidden by a question mark. We will refer to this as the masked bid vector. We will write b as (b i, b i ). Similarly, let v i denote the vector of all other agents valuation functions, T i = T n 1 be the space of those vectors. A strategy S i : T T is said to be a dominant strategy for agent i if u i (b i, S i (v i )) u i (b i, b i ) for all b i T i and b i, v i T. In other words, agent i s best strategy is to report her valuation as S i (v i ) whenever her true valuation is v i. A mechanism is said to be a dominant strategy mechanism if every agent has a dominant strategy. Definition (Truthful Mechanism) A truthful mechanism is a dominant strategy mechanism in which truth-telling is a dominant strategy for every agent, i.e. u i (b i, v i ) u i (b i, b i ) b i T i and b i, v i T Theorem (Bid-independence principle) If the mechanism (O,P) is truthful, and O(b i, b i ) = O(b i, b i ), then P i(b i, b i ) = P i (b i, b i ). 2

3 Proof: Suppose to the contrary, i.e. P i (b i, b i ) > P i (b i, b i ), while O(b i, b i ) = O(b i, b i ). When v i = b i and all the other agents bid b i, agent i is better off lying and bidding b i, contradicting truthfulness. This principle asserts that in a truthful mechanism, the bid of an agent affects the payment made by the agent only through its effect on the outcome of the mechanism Truthfulness as a Means to Simplified Bidding As mentioned earlier, we would like to construct mechanisms for selling advertising space on Internet web sites under which it is easy for the advertisers to determine their optimal bidding strategies. Unless an advertiser has a dominant strategy, she would be forced to speculate (or hire someone to speculate for her) on how the other advertisers are going to bid in order to determine her optimal strategy. Thus, in order to get rid of speculation and keep the process of bidding simple, we would like each advertiser to have a dominant strategy, i.e. we would like to use a dominant strategy mechanism. The Revelation principle stated below allows us to restrict our attention to truthful mechanisms without missing any possible combination of outcome and payment functions (when we view the outcome and payment as a function of valuation rather than bids). Theorem (Revelation principle [5, 6]) Every dominant strategy mechanism can be converted to a truthful mechanism without changing the outcome or the payments on vector of valuation functions of all agents. Proof: Given a dominant strategy mechanism M, construct a truthful mechanism M that simulates each bidder s dominant strategy in M. Let S i be agent i s dominant strategy under M. Then, M produces the same outcome and payments on bid vector b as the mechanism M produces on the bid vector (S i (b i )) i N. Clearly, agent i s dominant strategy under M is to bid b i = v i, because this is equivalent to playing the dominant strategy S i (v i ) in M The Vickrey Auction We next give an example of a classical truthful mechanism due to Vickrey [7]. Given the nature of its payment scheme, it is also called the second-price auction. It is used for selling a single item; so the outcome consists of the item being given to one of the agents. The valuation functions of the agents take a very simple form: if an agent gets the item, her valuation of the outcome is v i (here we are slightly abusing notation by using the term v i to refer to a single number); otherwise her valuation of the outcome is 0. The auction consists of inviting bids for the item, and giving the item to the highest bidder and charging her an amount equal to the second-highest bid. If two bidders tie for the highest bid, the item goes to the bidder with the lower index. Theorem The Vickrey auction is truthful. Proof: In order to prove truthfulness, we have to show that none of the bidders can benefit by not revealing her true valuation function. Fix an agent i and let h be the highest bid among the other agents. If v i > h, then the agent gets the item for an amount h whenever she bids an amount higher than h (which includes bidding her true valuation function). In this case, her utility is v i h. 3

4 The only possible way she can change the outcome is by bidding no more than h in which case her utility is 0. On the other hand, if v i h, she makes a profit of 0 as long as she bids h or less (which includes bidding her true valuation). She can possibly change the outcome by raising her bid above h, in which case her utility becomes negative. This shows that bidder i cannot benefit by not bidding her true valuation The Vickrey-Clarke-Groves Mechanism The most celebrated result in truthful mechanism design is the Vickrey-Clarke-Groves (VCG) mechanism [7]. It is a generalization of the Vickrey auction and can be used when the goal of a mechanism is to maximize the total valuation of all the agents. The VCG mechanism (O, P ) is given by: O(b) = o where o argmax o O P i (b) = j i b j (o ) + h i (b i ) b i (o) i N where the functions h i are arbitrary. That is, VCG selects the outcome that maximizes the total reported valuation, and charges agent i an amount P i that depends on b i only through its influence on the outcome o, just as required by bid-independence principle. Since the h i terms in the payment are completely independent of agent i s bid, they are irrelevant to truthfulness. The term j i b j(o ) in the payment is quite special though it aligns the utility function of agent i with the utilitarian objective function. This makes the mechanism truthful, as asserted by the following theorem. Theorem The VCG mechanism is truthful. The basic VCG mechanism can be augmented by weighting the agents differently and adding a bias to the outcome function, while preserving truthfulness [3, 4]. More formally, let w R n + be a set of non-negative weights. Let H : O R be a bias function. The resulting weighted, biased VCG mechanism is defined by : O(b) = o where o argmax w j b j (o) + H(o) j N o O P i (b) = 1 w j b j (o ) + H(o ) + h i (b i ) when > 0 j i P i (b) = H(o ) + h i (b i ) when = 0 where the functions h i are arbitrary. Theorem For every choice of weights and bias function, the weighted, biased VCG mechanism is truthful. 4

5 Proof: Clearly when the weight of agent i is zero, agent i has no incentive for being untruthful. When > 0, then there are two possibilities agent i is truthful, or agent i is untruthful. Assume that the output of the mechanism is o when i is truthful and it is o when i is untruthful. Then, o argmax v i (o) + w j b j (o) + H(o) and o argmax b i (o) + w j b j (o) + H(o) o O j N, j i o O j N, j i where v i is the true valuation function of agent i and b i is any other valuation function. Next we compute the utilities of agent i for outcomes o and o. u i (o ) = v i (o ) P i (b) = v i (o ) + 1 w j b j (o ) + H(o ) + h i (b i ) j i = 1 v i (o ) + w j b j (o ) + H(o ) + h i (b i ) j i Similarly, u i (o ) = 1 v i (o ) + w j b j (o ) + H(o ) + h i (b i ) j i The manner in which o has been chosen makes it clear that u i (o ) u i (o ). Therefore, the agent has no incentive for bidding untruthfully Weaknesses of VCG Mechanism Despite the attractiveness of the dominant-strategy property, the VCG mechanism also has several possible weaknesses [8]. low(or zero) auctioneer revenues. non-monotonicity of the auctioneer s revenues in the set of bidders and the amount of bid. vulnerability to collusion by a coalition of losing bidders. vulnerability to the use of multiple bidding identities by a single bidder The Search Engine Problem Consider a web page with slots where advertisements are displayed. Whenever the web page is accessed by an Internet user, the web site owner can choose to show her advertisements. 5

7 Assumptions In sponsored search, we typically work with K N. However, this can be easily generalized to the case with K N by reducing the number of slots K to N and adding dummy merchants with all relevant parameters set to 0. Slots are ordered so that the probability of clicks going through is higher for slots ranked higher. CTR i,j is arbitrary and non-increasing in j. In most cases, the auctioneer is aware of the Click Through Rates. v i is known to merchant i, but not to the auctioneer. The merchants are ranked in the order of decreasing b i. The merchants are risk-neutral. We formally define the next-price auctions as follows Definition (Next-price Auction) Given the rank function, R = (w 1, w 2,, w n ) and the bid vector b = (b 1,, b n ), the next-price auction ranks the merchants in the decreasing order of b i and charges the merchant ranked i an amount-per-click equal to the minimum bid she needs to have submitted in order to retain rank i. Then the price charged to the merchant ranked i is p i = +1b i+1. Note : Setting = 1 for all i is equivalent to the direct ranking function (the Overture model), while setting = CTR i,1 reduces to the revenue-ranking function (the Google model). In order to model the Click-through rates, we assume that they can be separated into a merchantspecific factor and a position-specific factor. Definition (Separable Click-through Rates) The click-through rates are said to be separable if there exist µ 1, µ 2,, µ n > 0 and θ 0 θ 2 θ K > 0 such that the click-through rate CTR i,j of the i th merchant at the j th slot is given by µ i θ j Need for a New Auction In this section, we provide the motivation for designing a new auction by showing that the nextprice auctions being currently used by Google and Yahoo! are not truthful. In order to reiterate the shortcomings of the VCG mechanism, we give instances of ranking functions for which there does not exist any set of weights and biases for which the ranking output by the VCG mechanism is always the same as the output by the given ranking function. 7

8 Next-price Auction is not Truthful Consider the following example. Three merchants A, B and C bidding for two slots. All of them have a click through rate of 0.5 at the top slot and 0.4 at the bottom slot. The true valuations per click of the three merchants be 200, 180 and 100 respectively. If all the merchants bid truthfully, merchant A ends up paying a price of 180 per click, making an expected profit of ( ) 0.5 = 10. In this case, she has an incentive to under cut B by lowering her bid to 110, and make a net profit of ( ) 0.4 = 40. Clearly, there is no incentive to bid higher than ones true valuation under the next-price auction. This is because the price-per-click charged is the minimum bid required to retain one s rank. Therefore in cases where bidding higher improves one s rank, the price-per-click charged is higher than one s true valuation Weighted VCG may not Always Apply In this section, we show by means of a counter-example that even for the simple case of direct ranking, there does not exist any set of (bid-independent) weights and biases for which the VCG solution achieves the same allocation as direct ranking. This will show that, in general, VCG does not apply to our problem. Consider the following example. Two merchants A and B bidding for two slots. Merchant A has a click-through rate of 0.4 at both the first and the second slot. Merchant B has a click-through rate of 0.4 at the first slot and 0.2 at the second slot. Since any of the merchants can bid the highest and get the top slot in direct ranking, both the merchants must have non-zero weight in order for weighted VCG to achieve the same allocation as direct ranking. Let w A > 0 and w B > 0 be the weights assigned by the VCG mechanism to merchants A and B respectively. H(x, y) denotes the bias assigned to ranking merchant x followed by y for x, y {A, B}. Then the VCG mechanism will rank B before A if w A (0.4b A ) + w B (0.4b B ) + H(B, A) > w A (0.4b A ) + w B (0.2b B ) + H(A, B). This is true whenever b B > H(A, B) H(B, A) 0.2w B, 8

9 Hence, the ranking of the merchants by VCG does not depend on A s bid. However, the direct ranking scheme will rank A before B whenever A s bid is higher than B s bid. Thus, the VCG mechanism does not apply to this example. We formally state (without proof) a few more shortcomings of the VCG auction. (For proof, see [1].) Theorem Let the number of merchants with non-zero click-through rates be n > K. If the click-through rates are not separable, then there exists a ranking function R = (w 1, w 2,, w n ) for which there does not exist any set of weights for which unbiased, weighted VCG always yields the same ranking as the ranking function R. Theorem Let the number of merchants with non-zero click-through rates be n > K. If the click-through rates are not separable, then there exists a ranking function R = (w 1, w 2,, w n ) for which there does not exist any set of weights for which biased. weighted VCG always yields the same ranking as the R. Theorem Let the click-through rates be separable. Then the VCG mechanism having merchant i s VCG weight set to always produces the same ordering as the ranking function CTR i,1 (w 1,, w n ). The above theorem implies that with the separability assumption, the ranking functions maximize a certain global utility function. In particular, the revenue-ranking scheme maximize the total utility obtained by the merchants and the auctioneer The Truthful Auction We will assume without loss of generality that the i th merchant also has the i th rank in the auction. The truthful auction is quite simple: For j i K, set the price-per-click p i charged to merchant i as: In other words, p i = K j=i (CTR i,j CTR i,j+1 ) w j+1 b j+1 ( ) 1. For those clicks which merchant i would have received at position i + 1, she pays the same price as she would have paid at position i For the additional clicks, merchant i pays an amount equal to the bid value of merchant i + 1. Since b i w j b j for j > i, it follows that p i b i. Hence the price charged per click-through can be no larger than the submitted bid. We will refer to this auction as Laddered Auction(w 1,, w n ) Analysis For the Laddered Auction(w 1,, w n ), we state the following theorem without proof. (For proof, see [1].) 9

10 Theorem Given fixed w 1,, w n, the Laddered Auction(w 1,, w n ) is truthful. Further, it is the unique truthful auction that ranks according to decreasing b i. Corollary For any fixed w 1,, w n, the Laddered Auction(w 1,, w n ) is the profitmaximizing truthful auction that ranks merchants by decreasing b i. References [1] Gagan Aggarwal. Privacy Protection and Advertising in a Networked World. PhD. Thesis, 2005 [2] N. Nisan, and A. Ronen. Algorithmic mechanism design. In Proceedings of the 31st Annual ACM Symposium on Theory of Computing, [3] J. Green, and J. Laffont. Characterization of satisfactory mechanisms for the revelation of preferences for public goods. In Econometrica, [4] K. Roberts. The characterization of implementable choice rules. In J. Laffont, editor, Aggregation and Revelation of Preferences, North Holland Publishing Company, [5] P. Dasgupta, P. Hammond, and E. Maskin. The implementation of social choice rules: Some results on incentive compatibility. In Review of Economic Studies, 1979 [6] R. Myerson. Incentive compatibility and the bargaining problem. In Econometrica, [7] W. Vickrey. Counterspeculation, auctions and competitive sealed tenders. In Journal of Finance, 1961 [8] Lawrence M. Ausubel, and Paul Milgrom. The Lovely but Lonely Vickrey Auction. In Combinatorial Auctions,

### Chapter 7. Sealed-bid Auctions

Chapter 7 Sealed-bid Auctions An auction is a procedure used for selling and buying items by offering them up for bid. Auctions are often used to sell objects that have a variable price (for example oil)

### A Simple Characterization for Truth-Revealing Single-Item Auctions

A Simple Characterization for Truth-Revealing Single-Item Auctions Kamal Jain 1, Aranyak Mehta 2, Kunal Talwar 3, and Vijay Vazirani 2 1 Microsoft Research, Redmond, WA 2 College of Computing, Georgia

### Internet Advertising and the Generalized Second Price Auction:

Internet Advertising and the Generalized Second Price Auction: Selling Billions of Dollars Worth of Keywords Ben Edelman, Harvard Michael Ostrovsky, Stanford GSB Michael Schwarz, Yahoo! Research A Few

Computational Learning Theory Spring Semester, 2009/10 Lecture 11: Sponsored search Lecturer: Yishay Mansour Scribe: Ben Pere, Jonathan Heimann, Alon Levin 11.1 Sponsored Search 11.1.1 Introduction Search

### Contract Auctions for Sponsored Search

Contract Auctions for Sponsored Search Sharad Goel, Sébastien Lahaie, and Sergei Vassilvitskii Yahoo! Research, 111 West 40th Street, New York, New York, 10018 Abstract. In sponsored search auctions advertisers

### Online Ad Auctions. By Hal R. Varian. Draft: February 16, 2009

Online Ad Auctions By Hal R. Varian Draft: February 16, 2009 I describe how search engines sell ad space using an auction. I analyze advertiser behavior in this context using elementary price theory and

### Chapter 15. Sponsored Search Markets. 15.1 Advertising Tied to Search Behavior

From the book Networks, Crowds, and Markets: Reasoning about a Highly Connected World. By David Easley and Jon Kleinberg. Cambridge University Press, 2010. Complete preprint on-line at http://www.cs.cornell.edu/home/kleinber/networks-book/

### Multi-unit auctions with budget-constrained bidders

Multi-unit auctions with budget-constrained bidders Christian Borgs Jennifer Chayes Nicole Immorlica Mohammad Mahdian Amin Saberi Abstract We study a multi-unit auction with multiple agents, each of whom

### Considerations of Modeling in Keyword Bidding (Google:AdWords) Xiaoming Huo Georgia Institute of Technology August 8, 2012

Considerations of Modeling in Keyword Bidding (Google:AdWords) Xiaoming Huo Georgia Institute of Technology August 8, 2012 8/8/2012 1 Outline I. Problem Description II. Game theoretical aspect of the bidding

### Cost of Conciseness in Sponsored Search Auctions

Cost of Conciseness in Sponsored Search Auctions Zoë Abrams Yahoo!, Inc. Arpita Ghosh Yahoo! Research 2821 Mission College Blvd. Santa Clara, CA, USA {za,arpita,erikvee}@yahoo-inc.com Erik Vee Yahoo! Research

### On the interest of introducing randomness in ad-word auctions

On the interest of introducing randomness in ad-word auctions Patrick Maillé 1 and Bruno Tuffin 2 1 Institut Telecom; Telecom Bretagne 2 rue de la Châtaigneraie CS 17607 35576 Cesson Sévigné Cedex, France

### Cournot s model of oligopoly

Cournot s model of oligopoly Single good produced by n firms Cost to firm i of producing q i units: C i (q i ), where C i is nonnegative and increasing If firms total output is Q then market price is P(Q),

### CPC/CPA Hybrid Bidding in a Second Price Auction

CPC/CPA Hybrid Bidding in a Second Price Auction Benjamin Edelman Hoan Soo Lee Working Paper 09-074 Copyright 2008 by Benjamin Edelman and Hoan Soo Lee Working papers are in draft form. This working paper

### ECON 459 Game Theory. Lecture Notes Auctions. Luca Anderlini Spring 2015

ECON 459 Game Theory Lecture Notes Auctions Luca Anderlini Spring 2015 These notes have been used before. If you can still spot any errors or have any suggestions for improvement, please let me know. 1

### Internet Advertising and the Generalized Second-Price Auction: Selling Billions of Dollars Worth of Keywords

Internet Advertising and the Generalized Second-Price Auction: Selling Billions of Dollars Worth of Keywords by Benjamin Edelman, Michael Ostrovsky, and Michael Schwarz (EOS) presented by Scott Brinker

An Introduction to Sponsored Search Advertising Susan Athey Market Design Prepared in collaboration with Jonathan Levin (Stanford) Sponsored Search Auctions Google revenue in 2008: \$21,795,550,000. Hal

### Internet Advertising and the Generalized Second Price Auction: Selling Billions of Dollars Worth of Keywords

Internet Advertising and the Generalized Second Price Auction: Selling Billions of Dollars Worth of Keywords Benjamin Edelman Harvard University bedelman@fas.harvard.edu Michael Ostrovsky Stanford University

### Algorithmic Mechanism Design for Load Balancing in Distributed Systems

In Proc. of the 4th IEEE International Conference on Cluster Computing (CLUSTER 2002), September 24 26, 2002, Chicago, Illinois, USA, IEEE Computer Society Press, pp. 445 450. Algorithmic Mechanism Design

### Economic background of the Microsoft/Yahoo! case

Economic background of the Microsoft/Yahoo! case Andrea Amelio and Dimitrios Magos ( 1 ) Introduction ( 1 ) This paper offers an economic background for the analysis conducted by the Commission during

Advertisement Allocation for Generalized Second Pricing Schemes Ashish Goel Mohammad Mahdian Hamid Nazerzadeh Amin Saberi Abstract Recently, there has been a surge of interest in algorithms that allocate

### On Best-Response Bidding in GSP Auctions

08-056 On Best-Response Bidding in GSP Auctions Matthew Cary Aparna Das Benjamin Edelman Ioannis Giotis Kurtis Heimerl Anna R. Karlin Claire Mathieu Michael Schwarz Copyright 2008 by Matthew Cary, Aparna

### CITY UNIVERSITY OF HONG KONG. Revenue Optimization in Internet Advertising Auctions

CITY UNIVERSITY OF HONG KONG l ½ŒA Revenue Optimization in Internet Advertising Auctions p ]zwû ÂÃÙz Submitted to Department of Computer Science õò AX in Partial Fulfillment of the Requirements for the

### Mechanism Design for Federated Sponsored Search Auctions

Proceedings of the Twenty-Fifth AAAI Conference on Artificial Intelligence Mechanism Design for Federated Sponsored Search Auctions Sofia Ceppi and Nicola Gatti Dipartimento di Elettronica e Informazione

### Internet Advertising and the Generalized Second-Price Auction: Selling Billions of Dollars Worth of Keywords

Internet Advertising and the Generalized Second-Price Auction: Selling Billions of Dollars Worth of Keywords By Benjamin Edelman, Michael Ostrovsky, and Michael Schwarz August 1, 2006 Abstract We investigate

### Sharing Online Advertising Revenue with Consumers

Sharing Online Advertising Revenue with Consumers Yiling Chen 2,, Arpita Ghosh 1, Preston McAfee 1, and David Pennock 1 1 Yahoo! Research. Email: arpita, mcafee, pennockd@yahoo-inc.com 2 Harvard University.

Introduction to Computational Advertising ISM293 University of California, Santa Cruz Spring 2009 Instructors: Ram Akella, Andrei Broder, and Vanja Josifovski 1 Questions about last lecture? We welcome

### Truthful Mechanisms for One-Parameter Agents

Truthful Mechanisms for One-Parameter Agents Aaron Archer Éva Tardos y Abstract In this paper, we show how to design truthful (dominant strategy) mechanisms for several combinatorial problems where each

### Bidding Dynamics of Rational Advertisers in Sponsored Search Auctions on the Web

Proceedings of the International Conference on Advances in Control and Optimization of Dynamical Systems (ACODS2007) Bidding Dynamics of Rational Advertisers in Sponsored Search Auctions on the Web S.

### Hybrid Auctions Revisited

Hybrid Auctions Revisited Dan Levin and Lixin Ye, Abstract We examine hybrid auctions with affiliated private values and risk-averse bidders, and show that the optimal hybrid auction trades off the benefit

### Monotone multi-armed bandit allocations

JMLR: Workshop and Conference Proceedings 19 (2011) 829 833 24th Annual Conference on Learning Theory Monotone multi-armed bandit allocations Aleksandrs Slivkins Microsoft Research Silicon Valley, Mountain

### A Study of Second Price Internet Ad Auctions. Andrew Nahlik

A Study of Second Price Internet Ad Auctions Andrew Nahlik 1 Introduction Internet search engine advertising is becoming increasingly relevant as consumers shift to a digital world. In 2010 the Internet

A Cascade Model for Externalities in Sponsored Search David Kempe 1 and Mohammad Mahdian 2 1 University of Southern California, Los Angeles, CA. clkempe@usc.edu 2 Yahoo! Research, Santa Clara, CA. mahdian@yahoo-inc.com

### Web Advertising 1 2/26/2013 CS190: Web Science and Technology, 2010

Web Advertising 12/26/2013 CS190: Web Science and Technology, 2010 Today's Plan Logistics Understanding searchers (Commercial Perspective) Search Advertising Next project: Google advertising challenge

### An Expressive Auction Design for Online Display Advertising. AUTHORS: Sébastien Lahaie, David C. Parkes, David M. Pennock

An Expressive Auction Design for Online Display Advertising AUTHORS: Sébastien Lahaie, David C. Parkes, David M. Pennock Li PU & Tong ZHANG Motivation Online advertisement allow advertisers to specify

### Expressive Auctions for Externalities in Online Advertising

Expressive Auctions for Externalities in Online Advertising ABSTRACT Arpita Ghosh Yahoo! Research Santa Clara, CA, USA arpita@yahoo-inc.com When online ads are shown together, they compete for user attention

### Truthful and Non-Monetary Mechanism for Direct Data Exchange

Truthful and Non-Monetary Mechanism for Direct Data Exchange I-Hong Hou, Yu-Pin Hsu and Alex Sprintson Department of Electrical and Computer Engineering Texas A&M University {ihou, yupinhsu, spalex}@tamu.edu

### Moral Hazard. Itay Goldstein. Wharton School, University of Pennsylvania

Moral Hazard Itay Goldstein Wharton School, University of Pennsylvania 1 Principal-Agent Problem Basic problem in corporate finance: separation of ownership and control: o The owners of the firm are typically

### Sharing Online Advertising Revenue with Consumers

Sharing Online Advertising Revenue with Consumers Yiling Chen 2,, Arpita Ghosh 1, Preston McAfee 1, and David Pennock 1 1 Yahoo! Research. Email: arpita, mcafee, pennockd@yahoo-inc.com 2 Harvard University.

### Optimal Auction Design and Equilibrium Selection in Sponsored Search Auctions

Optimal Auction Design and Equilibrium Selection in Sponsored Search Auctions Benjamin Edelman Michael Schwarz Working Paper 10-054 Copyright 2010 by Benjamin Edelman and Michael Schwarz Working papers

### Should Ad Networks Bother Fighting Click Fraud? (Yes, They Should.)

Should Ad Networks Bother Fighting Click Fraud? (Yes, They Should.) Bobji Mungamuru Stanford University bobji@i.stanford.edu Stephen Weis Google sweis@google.com Hector Garcia-Molina Stanford University

### Optimal slot restriction and slot supply strategy in a keyword auction

WIAS Discussion Paper No.21-9 Optimal slot restriction and slot supply strategy in a keyword auction March 31, 211 Yoshio Kamijo Waseda Institute for Advanced Study, Waseda University 1-6-1 Nishiwaseda,

### A Theory of Auction and Competitive Bidding

A Theory of Auction and Competitive Bidding Paul Milgrom and Rober Weber Econometrica 1982 Presented by Yifang Guo Duke University November 3, 2011 Yifang Guo (Duke University) Envelope Theorems Nov. 3,

### Keyword Auctions as Weighted Unit-Price Auctions

Keyword Auctions as Weighted Unit-Price Auctions De Liu Univ. of Kentucky Jianqing Chen Univ. of Texas at Austin September 7, 2006 Andrew B. Whinston Univ. of Texas at Austin In recent years, unit-price

Sponsored Search with Contexts Eyal Even-Dar, Michael Kearns, and Jennifer Wortman Department of Computer and Information Science University of Pennsylvania Philadelphia, PA 1914 ABSTRACT We examine a

### Position Auctions with Externalities

Position Auctions with Externalities Patrick Hummel 1 and R. Preston McAfee 2 1 Google Inc. phummel@google.com 2 Microsoft Corp. preston@mcafee.cc Abstract. This paper presents models for predicted click-through

### Value of Learning in Sponsored Search Auctions

Value of Learning in Sponsored Search Auctions Sai-Ming Li 1, Mohammad Mahdian 1, and R. Preston McAfee 1 Yahoo! Inc. Santa Clara, CA, USA. Abstract. The standard business model in the sponsored search

### each college c i C has a capacity q i - the maximum number of students it will admit

n colleges in a set C, m applicants in a set A, where m is much larger than n. each college c i C has a capacity q i - the maximum number of students it will admit each college c i has a strict order i

### Equilibrium Bids in Sponsored Search. Auctions: Theory and Evidence

Equilibrium Bids in Sponsored Search Auctions: Theory and Evidence Tilman Börgers Ingemar Cox Martin Pesendorfer Vaclav Petricek September 2008 We are grateful to Sébastien Lahaie, David Pennock, Isabelle

### 1.4 Hidden Information and Price Discrimination 1

1.4 Hidden Information and Price Discrimination 1 To be included in: Elmar Wolfstetter. Topics in Microeconomics: Industrial Organization, Auctions, and Incentives. Cambridge University Press, new edition,

### Optimal Auctions Continued

Lecture 6 Optimal Auctions Continued 1 Recap Last week, we... Set up the Myerson auction environment: n risk-neutral bidders independent types t i F i with support [, b i ] residual valuation of t 0 for

### arxiv:1112.0829v1 [math.pr] 5 Dec 2011

How Not to Win a Million Dollars: A Counterexample to a Conjecture of L. Breiman Thomas P. Hayes arxiv:1112.0829v1 [math.pr] 5 Dec 2011 Abstract Consider a gambling game in which we are allowed to repeatedly

### Click efficiency: a unified optimal ranking for online Ads and documents

DOI 10.1007/s10844-015-0366-3 Click efficiency: a unified optimal ranking for online Ads and documents Raju Balakrishnan 1 Subbarao Kambhampati 2 Received: 21 December 2013 / Revised: 23 March 2015 / Accepted:

### Bayesian Nash Equilibrium

. Bayesian Nash Equilibrium . In the final two weeks: Goals Understand what a game of incomplete information (Bayesian game) is Understand how to model static Bayesian games Be able to apply Bayes Nash

### IN CURRENT distributed systems such as computational

IEEE TRANSACTIONS ON SYSTEMS, MAN, AND CYBERNETICS PART B: CYBERNETICS, VOL. 34, NO. 1, FEBRUARY 2004 77 Algorithmic Mechanism Design for Load Balancing in Distributed Systems Daniel Grosu, Student Member,

### Sponsored Search. Corsi di Laurea Specialistica in Ingegneria Informatica/Gestionale. Corso di Sistemi Informativi per il Web A.A.

Corsi di Laurea Specialistica in Ingegneria Informatica/Gestionale Corso di Sistemi Informativi per il Web A.A. 2005 2006 Sponsored Search Game Theory Azzurra Ragone Sponsored Search Results in Google

### α = u v. In other words, Orthogonal Projection

Orthogonal Projection Given any nonzero vector v, it is possible to decompose an arbitrary vector u into a component that points in the direction of v and one that points in a direction orthogonal to v

### Regret Minimization for Reserve Prices in Second-Price Auctions

Regret Minimization for Reserve Prices in Second-Price Auctions Nicolò Cesa-Bianchi Università degli Studi di Milano Joint work with: Claudio Gentile (Varese) and Yishay Mansour (Tel-Aviv) N. Cesa-Bianchi

EFFECTIVE ONLINE ADVERTISING by Hamed Sadeghi Neshat B.Sc., Sharif University of Technology, Tehran, Iran, 2009 a Thesis submitted in partial fulfillment of the requirements for the degree of Master of

### A dynamic auction for multi-object procurement under a hard budget constraint

A dynamic auction for multi-object procurement under a hard budget constraint Ludwig Ensthaler Humboldt University at Berlin DIW Berlin Thomas Giebe Humboldt University at Berlin March 3, 2010 Abstract

### Optimal Auctions. Jonathan Levin 1. Winter 2009. Economics 285 Market Design. 1 These slides are based on Paul Milgrom s.

Optimal Auctions Jonathan Levin 1 Economics 285 Market Design Winter 29 1 These slides are based on Paul Milgrom s. onathan Levin Optimal Auctions Winter 29 1 / 25 Optimal Auctions What auction rules lead

### Vickrey-Dutch Procurement Auction for Multiple Items

Vickrey-Dutch Procurement Auction for Multiple Items Debasis Mishra Dharmaraj Veeramani First version: August 2004, This version: March 2006 Abstract We consider a setting where there is a manufacturer

### Two-Sided Matching Theory

Two-Sided Matching Theory M. Utku Ünver Boston College Introduction to the Theory of Two-Sided Matching To see which results are robust, we will look at some increasingly general models. Even before we

### Offline 1-Minesweeper is NP-complete

Offline 1-Minesweeper is NP-complete James D. Fix Brandon McPhail May 24 Abstract We use Minesweeper to illustrate NP-completeness proofs, arguments that establish the hardness of solving certain problems.

### arxiv:1209.0832v1 [cs.gt] 4 Sep 2012

Coopetitive Ad Auctions Darrell Hoy Kamal Jain Christopher A. Wilkens arxiv:1209.0832v1 [cs.gt] 4 Sep 2012 Abstract A single advertisement often benefits many parties, for example, an ad for a Samsung

### Discrete Strategies in Keyword Auctions and their Inefficiency for Locally Aware Bidders

Discrete Strategies in Keyword Auctions and their Inefficiency for Locally Aware Bidders Evangelos Markakis Orestis Telelis Abstract We study formally two simple discrete bidding strategies in the context

### Reserve Prices in Internet Advertising Auctions: A Field Experiment

Reserve Prices in Internet Advertising Auctions: A Field Experiment Michael Ostrovsky Stanford University ostrovsky@gsb.stanford.edu Michael Schwarz Yahoo! Labs mschwarz@yahoo-inc.com December 24, 2009

### Second degree price discrimination

Bergals School of Economics Fall 1997/8 Tel Aviv University Second degree price discrimination Yossi Spiegel 1. Introduction Second degree price discrimination refers to cases where a firm does not have

### Click Fraud Resistant Methods for Learning Click-Through Rates

Click Fraud Resistant Methods for Learning Click-Through Rates Nicole Immorlica, Kamal Jain, Mohammad Mahdian, and Kunal Talwar Microsoft Research, Redmond, WA, USA, {nickle,kamalj,mahdian,kunal}@microsoft.com

### How to Price Shared Optimizations in the Cloud

How to Price Shared Optimizations in the Cloud Prasang Upadhyaya, Magdalena Balazinska, and Dan Suciu Department of Computer Science and Engineering, University of Washington, Seattle, WA, USA {prasang,

### Advertising in Google Search Deriving a bidding strategy in the biggest auction on earth.

Advertising in Google Search Deriving a bidding strategy in the biggest auction on earth. Anne Buijsrogge Anton Dijkstra Luuk Frankena Inge Tensen Bachelor Thesis Stochastic Operations Research Applied

### Alok Gupta. Dmitry Zhdanov

RESEARCH ARTICLE GROWTH AND SUSTAINABILITY OF MANAGED SECURITY SERVICES NETWORKS: AN ECONOMIC PERSPECTIVE Alok Gupta Department of Information and Decision Sciences, Carlson School of Management, University

### Unraveling versus Unraveling: A Memo on Competitive Equilibriums and Trade in Insurance Markets

Unraveling versus Unraveling: A Memo on Competitive Equilibriums and Trade in Insurance Markets Nathaniel Hendren January, 2014 Abstract Both Akerlof (1970) and Rothschild and Stiglitz (1976) show that

Master Thesis A Bidding Strategy of Intermediary in Display Advertisement Auctions Supervisor Associate Professor Shigeo MATSUBARA Department of Social Informatics Graduate School of Informatics Kyoto

### Information in Mechanism Design

Dirk Bergemann and Juuso Valimaki Econometric Society World Congress August 2005 Mechanism Design Economic agents have private information that is relevant for a social allocation problem. Information

### 8 Modeling network traffic using game theory

8 Modeling network traffic using game theory Network represented as a weighted graph; each edge has a designated travel time that may depend on the amount of traffic it contains (some edges sensitive to

### Invited Applications Paper

Invited Applications Paper - - Thore Graepel Joaquin Quiñonero Candela Thomas Borchert Ralf Herbrich Microsoft Research Ltd., 7 J J Thomson Avenue, Cambridge CB3 0FB, UK THOREG@MICROSOFT.COM JOAQUINC@MICROSOFT.COM

### Competition and Fraud in Online Advertising Markets

Competition and Fraud in Online Advertising Markets Bob Mungamuru 1 and Stephen Weis 2 1 Stanford University, Stanford, CA, USA 94305 2 Google Inc., Mountain View, CA, USA 94043 Abstract. An economic model

### Practical Guide to the Simplex Method of Linear Programming

Practical Guide to the Simplex Method of Linear Programming Marcel Oliver Revised: April, 0 The basic steps of the simplex algorithm Step : Write the linear programming problem in standard form Linear

### Pricing Ad Slots with Consecutive Multi-unit Demand

Pricing Ad Slots with Consecutive Multi-unit Demand Xiaotie Deng 1,2, Paul Goldberg 2, Yang Sun 3, Bo Tang 2, and Jinshan Zhang 2 1 Department of Computer Science, Shanghai Jiao Tong University, China

### On Multiple Keyword Sponsored Search Auctions with Budgets

On Multiple Keyword Sponsored Search Auctions with Budgets Riccardo Colini-Baldeschi 1,, Monika Henzinger 2,, Stefano Leonardi 1,, and Martin Starnberger 2, 1 Sapienza University of Rome, Italy 2 University

### Frequency Capping in Online Advertising

Frequency Capping in Online Advertising Niv Buchbinder Moran Feldman Arpita Ghosh Joseph (Seffi) Naor July 2, 2014 Abstract We study the following online problem. There are n advertisers. Each advertiser

### Pay-per-action model for online advertising

Pay-per-action model for online advertising Mohammad Mahdian 1 and Kerem Tomak 1 Yahoo! Research. Email: {mahdian,kerem}@yahoo-inc.com Abstract. The online advertising industry is currently based on two

### A Load Balancing Mechanism with Verification

A Load Balancing Mechanism with Verification Daniel Grosu and Anthony T. Chronopoulos Department of Computer Science, University of Texas at San Antonio, 6900 N. Loop 1604 West, San Antonio, TX 78249 dgrosu,

Online Adwords Allocation Shoshana Neuburger May 6, 2009 1 Overview Many search engines auction the advertising space alongside search results. When Google interviewed Amin Saberi in 2004, their advertisement

### The Role of Priorities in Assigning Indivisible Objects: A Characterization of Top Trading Cycles

The Role of Priorities in Assigning Indivisible Objects: A Characterization of Top Trading Cycles Atila Abdulkadiroglu and Yeon-oo Che Duke University and Columbia University This version: November 2010

### A survey on click modeling in web search

A survey on click modeling in web search Lianghao Li Hong Kong University of Science and Technology Outline 1 An overview of web search marketing 2 An overview of click modeling 3 A survey on click models

Christmas Gift Exchange Games Arpita Ghosh 1 and Mohammad Mahdian 1 Yahoo! Research Santa Clara, CA, USA. Email: arpita@yahoo-inc.com, mahdian@alum.mit.edu Abstract. The Christmas gift exchange is a popular

### Part II: Bidding, Dynamics and Competition. Jon Feldman S. Muthukrishnan

Part II: Bidding, Dynamics and Competition Jon Feldman S. Muthukrishnan Campaign Optimization Budget Optimization (BO): Simple Input: Set of keywords and a budget. For each keyword, (clicks, cost) pair.

### Schooling, Political Participation, and the Economy. (Online Supplementary Appendix: Not for Publication)

Schooling, Political Participation, and the Economy Online Supplementary Appendix: Not for Publication) Filipe R. Campante Davin Chor July 200 Abstract In this online appendix, we present the proofs for

### Mechanism Design for Multi-Agent Meeting Scheduling

Mechanism Design for Multi-Agent Meeting Scheduling Elisabeth Crawford and Manuela Veloso Computer Science Department, Carnegie Mellon University, Pittsburgh, PA, 15213 {ehc,mmv}@cs.cmu.edu Abstract In

### A Simple Model of Price Dispersion *

Federal Reserve Bank of Dallas Globalization and Monetary Policy Institute Working Paper No. 112 http://www.dallasfed.org/assets/documents/institute/wpapers/2012/0112.pdf A Simple Model of Price Dispersion

### Branding and Search Engine Marketing

Branding and Search Engine Marketing Abstract The paper investigates the role of paid search advertising in delivering optimal conversion rates in brand-related search engine marketing (SEM) strategies.

### Anonymous Pricing of Efficient Allocations in Combinatorial Economies

Anonymous Pricing of Efficient Allocations in Combinatorial Economies Wolfram Conen FH Gelsenkirchen 45877 Gelsenkirchen, Germany E-mail: conen@gmx.de Tuomas Sandholm Carnegie Mellon University Computer

### 1 Introduction. Linear Programming. Questions. A general optimization problem is of the form: choose x to. max f(x) subject to x S. where.

Introduction Linear Programming Neil Laws TT 00 A general optimization problem is of the form: choose x to maximise f(x) subject to x S where x = (x,..., x n ) T, f : R n R is the objective function, S

### 1. (First passage/hitting times/gambler s ruin problem:) Suppose that X has a discrete state space and let i be a fixed state. Let

Copyright c 2009 by Karl Sigman 1 Stopping Times 1.1 Stopping Times: Definition Given a stochastic process X = {X n : n 0}, a random time τ is a discrete random variable on the same probability space as

### MATH10212 Linear Algebra. Systems of Linear Equations. Definition. An n-dimensional vector is a row or a column of n numbers (or letters): a 1.

MATH10212 Linear Algebra Textbook: D. Poole, Linear Algebra: A Modern Introduction. Thompson, 2006. ISBN 0-534-40596-7. Systems of Linear Equations Definition. An n-dimensional vector is a row or a column

### ALMOST COMMON PRIORS 1. INTRODUCTION

ALMOST COMMON PRIORS ZIV HELLMAN ABSTRACT. What happens when priors are not common? We introduce a measure for how far a type space is from having a common prior, which we term prior distance. If a type