How does the market of How does the market of sponsored sponsored links operate? links operate?

User enters a query

The auction for the link to appear on

the search results page takes place

Advertisements of the highest bidders

are displayed as sponsored links along

the search results

If the sponsored link is clicked upon

the advertiser pays a provider for

bringing the user to her webpage

Advertiser submits a bid for slot for the targeted keywords

Advertiser pays amount corresponding to a bid of the highest ranked competitor below her

Valuation (v) bid (u)

bids are weighted byclick through rates

slots are assigned by weighted bid order

Generalized second price auction

Sponsored Links in Search auctionsSponsored Links in Search auctions

Specifics: Specifics: Multiple non-equivalent items are auctioned simultaneouslyDifferent definition of internet ad-unit for bidders and ad-

platform Large number of bidders competing in large number of actions which cost very little

Mean field approximationMean field approximationMarkov Decision Process

Decision Maker

Unobservable

Gaing(i)

))

))

P. Key et al, working paper

cost

Value function:

Bidd

ing

with

bud

gets

Optimal Control Theorem

• From the point of the optimizing bidder, GSP can be interpreted as a stand-alone standard auction on which the bidder assigns a virtual valuation which is shaded down

• Mean field approximation simplifies models for online-bidding making optimization and control tractable

• MFE exists for on-line single-slot bidding with budgets • MFE exists in special cases of online bidding without

budgets constraints, but, in general, MFE may not exists• Outlook: Modelling beyond mean field