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Dynamic stochastic modelling of online generalised second price auctions (GPS). N.Kudryashova,Cambridge University P. Key, Microsoft Research. How does the market of sponsored links operate?. User enters a query The auction for the link to appear on the search results page takes place

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Dynamic stochastic modelling of online generalised second price auctions gps

Dynamic stochastic modelling of online generalised second price auctions (GPS)

N.Kudryashova,Cambridge University

P. Key, Microsoft Research


How does the market of sponsored links operate
How does the market of price auctions (GPS)sponsored 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

Valuation (v)

bid (u)

bids are weighted by

click through rates

slots are assigned by

weighted bid order

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

Generalized second price auction


Sponsored links in search auctions
Sponsored Links in Search auctions price auctions (GPS)

Specifics: Multiple non-equivalent items are auctioned simultaneously

Different 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 approximation

Markov Decision Process


Dynamic stochastic modelling of online generalised second price auctions gps

P. Key et al, working paper price auctions (GPS)

Decision Maker

Unobservable

Bidding with budgets

))

cost

Gain

))

g(i)

Value function:


Optimal control theorem
Optimal Control Theorem price auctions (GPS)

  • 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


Dynamic stochastic modelling of online generalised second price auctions gps

  • 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