Mechanism Design in Sponsored Search Auction

Mechanism Design in Sponsored Search Auction Syrgkanis Vasileios

Outline • Introduction • Mechanisms • GFP • GSP • VCG • Laddered • Budgets • Conclusions

Ingredients • Advertiser-provided content • Advertiser-provided bids that value traffic on specified concepts or keywords. • Combining a manual and automated review process to ensure relevancy • Matching advertiser content to user search queries • Displaying advertiser content in some rank order in some placement alongside search engine results • Gathering data, metering clicks, and charging advertisers based on consumer clicks

Brief History • 1994 First Available Web Browser, First Banner Ads • 1998 GoTo (later Overture, now Yahoo): Pay-Per-Click GFP • 2002 AdWords: GSP

Model • N Bidders • M slots • Each Bidder has a private valuation vi and announces a public bid bi for acquiring a slot • Mechanism assigns a weight wi to each bidder • Assigns slots in decreasing WiBi and imposes payments pi • Bidders utility if ranked in slot j is CTRji(vi-pi)

Questions • What is wi ? • Rank-by-bid, Rank-by-Revenue • What is pi ? • GFP, GSP, VCG, Laddered

What’s the Game • Given the mechanism bidders play a game • Utility = Utility at the slot induced by the mechanism • Aspects of the game we are interested • Equilibria • Truthfulness • Efficiency • Profit-maximization

Notions of Equilibrium • Bayesian Nash • assumption of prior distribution of bidders valuations • Envy-free • Not just don’t want to change unilateraly but don’t want to exchange position with some other

Mechanisms • Generalised First Price (GFP) • Generalised Second Price (GSP) • Weighted VCG • Laddered

GFP • Simple: pi=bi • Characteristics • Admits Bayesian-Nash • May not admit pure strategy full information equilibria • Not truthfull • Unstable in the dynamic setting

GSP • Simple: pi=wi+1bi+1/wi • Characteristics • Admits Pure NE • Admits a Pure NE with payments equal to VCG • Admits a Locally Envy free Equilibrium • Bidders Best Envy free Eq. has ranking and payments equal to VCG • Not truthful

Weighted VCG • The known VCG mechanism applied to Sponsored Search • Every player pays the externalities that he has to others • Aggregate value of clicks of others when i not present – Aggregate value of clicks when present • Characteristics • Bidding truthfully is dominant strategy • Payments less than GSP for the same bids • May not always allocate according to wibi

VCG Example • 2 Bidders , 2 slots • Bidder A has CTR 0.4 for both slots • Bidder B has CTR 0.4 for first and 0.2 for second • Let wA and wB the weights of the merchants • Let H(x,y) the bias of VCG for ranking merchant x above y • B will be ranked above if • Irrespective of the bid of A

Laddered Auction • Complex • Given Fixed weights the laddered auction is the unique truthful auction that ranks according to decreasing wibi • Trivially: • It is the profit-maximizing truthful auction that ranks according to wibi

Laddered Auction (2) • Intuitively: • For clicks which merchant i would have received at position i+1, pays the same price she would pay at i+1 • For the additional clicks, she pays an amount equal to the minimum bid required to retain position i

Laddered Auction (3) • For separable CTRs, there exists an equilibrium of the GSP that yields the same revenue as the laddered auction. • The above can be reached by the following dynamics • Bidder >K bid truthfully • Bidder at K bids the amount that will prevent somebody from above to undercut him • This is done recursively in increasing order of i

TruthfulnessCannot gain by moving higher or lower 30 2nd slot 20 3rd slot Top slot 15 Bid/Valuation per click 4th slot 2nd slot 10 3rd slot 4th slot 0 15 20 30 50 Clicks/100 impressions

Budget Constraints • We have to insert in the initial model budget constraints • Every bidder places his bid bi and his budget constraint ci • Mechanism cannot charge him more than ci • As long as ci>bi the results in the one time auction examined remain the same since pi<bi for all mechanisms • In the dynamic environment budgets cannot be neglected

Multi-Unit Auctions with budgets • Multiple units of a good • Bidders give bids and budgets • Mechanism assigns goods • Each bidder can get one or more goods

Multi-Unit Auctions with budgets (2) • Consumer Sovereignty • Keeping constant the bids of other bidders there exists a bid and budget for i such that he will get all goods

Multi-Unit Auctions with budgets (2) • Independence of Irrelevant Alternatives • If a bidder gets no item when bidding (bi,ci) then the allocation when he bids (0,0) remains the same

Strong Non Bundling (2 units, 2 bidders) • For any strategy of the first player there exists a strategy for the second that allocates one unit to each bidder

Impossibility Result • There is no truthful auction for two bidders and two units that satisfies consumer sovereignty, IIA and strong non-bundling • However there exists an asymptotically optimal mechanism that doesn’t necessarily assign all units that is truthful

Conclusions (or how I see it) Academia Advertisers GFP GSP VCG Laddered

Open Questions • How can results of multi-unit item auctions be transferred to SSAs • Can we put the repeated nature of the auction to better use? • Better pricing models which take into account • budgets • information • slots

References • C. Borgs, J. Chayes, N. Immorlica, M. Mahdian, and A. Saberi. Multi-unit auctions with budget-constrained bidders. Proceedings of the 7th ACM Conference on Electronic Commerce, pages 44–51, 2005. • B. Edelman, M. Ostrovsky, and M. Schwarz. Internet advertising and the generalized second price auction: Selling billions of dollars worth of keywords. Workshop on Sponsored Search Auctions 2006. • G. Aggrawal, A. Goel, R. Motwani, Truthful Auctions for Pricing Search Keywords, EC 2006 • Nisan et al., Algorithmic Game Theory

Thank you!

Mechanism Design in Sponsored Search Auction