A glimpse to sponsored search auctions Maria Serna Fall 2016 - - PowerPoint PPT Presentation

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A glimpse to sponsored search auctions Maria Serna Fall 2016 - - PowerPoint PPT Presentation

Aug 29, 2022 210 likes •1.23k views

Keyword Auctions Basic model GSP auction A glimpse to sponsored search auctions Maria Serna Fall 2016 AGT-MIRI Sponsored search Keyword Auctions Basic model GSP auction 1 Keyword Auctions 2 Basic model 3 GSP auction AGT-MIRI Sponsored

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Keyword Auctions Basic model GSP auction

A glimpse to sponsored search auctions

Maria Serna Fall 2016

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Keyword Auctions Basic model GSP auction

1 Keyword Auctions 2 Basic model 3 GSP auction

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Keyword Auctions Basic model GSP auction

Keyword Auctions/ Sponsored search

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Keyword Auctions Basic model GSP auction

Keyword Auctions/ Sponsored search

Advertiser submit bids for keywords

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Keyword Auctions Basic model GSP auction

Keyword Auctions/ Sponsored search

Advertiser submit bids for keywords

Offer a dollar payment per click. Alternatives: price per impression, or per conversion.

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Keyword Auctions Basic model GSP auction

Keyword Auctions/ Sponsored search

Advertiser submit bids for keywords

Offer a dollar payment per click. Alternatives: price per impression, or per conversion.

Separate auction for every query

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Keyword Auctions Basic model GSP auction

Keyword Auctions/ Sponsored search

Advertiser submit bids for keywords

Offer a dollar payment per click. Alternatives: price per impression, or per conversion.

Separate auction for every query

Positions awarded by some mechanism. Advertisers get a price per click.

AGT-MIRI Sponsored search

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Keyword Auctions Basic model GSP auction

Keyword Auctions/ Sponsored search

Advertiser submit bids for keywords

Offer a dollar payment per click. Alternatives: price per impression, or per conversion.

Separate auction for every query

Positions awarded by some mechanism. Advertisers get a price per click.

Some new features

AGT-MIRI Sponsored search

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Keyword Auctions Basic model GSP auction

Keyword Auctions/ Sponsored search

Advertiser submit bids for keywords

Offer a dollar payment per click. Alternatives: price per impression, or per conversion.

Separate auction for every query

Positions awarded by some mechanism. Advertisers get a price per click.

Some new features

Multiple positions, but advertisers submit only a single bid. Search is highly targeted, and transaction oriented.

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Keyword Auctions Basic model GSP auction

Keyword auctions: evolution

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Keyword Auctions Basic model GSP auction

Keyword auctions: evolution

Pre-1994: advertising sold on a per-impression basis, traditional direct sales to advertisers.

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Keyword Auctions Basic model GSP auction

Keyword auctions: evolution

Pre-1994: advertising sold on a per-impression basis, traditional direct sales to advertisers. 1994: Overture (then GoTo) allows advertisers to bid for keywords, offering some amount per click. Advertisers pay their bids.

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Keyword Auctions Basic model GSP auction

Keyword auctions: evolution

Pre-1994: advertising sold on a per-impression basis, traditional direct sales to advertisers. 1994: Overture (then GoTo) allows advertisers to bid for keywords, offering some amount per click. Advertisers pay their bids. Late 1990s: Yahoo! and MSN adopt Overture, but mechanism proves unstable. Advertisers constantly change bids to avoid paying more than necessary.

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Keyword Auctions Basic model GSP auction

Keyword auctions: evolution

Pre-1994: advertising sold on a per-impression basis, traditional direct sales to advertisers. 1994: Overture (then GoTo) allows advertisers to bid for keywords, offering some amount per click. Advertisers pay their bids. Late 1990s: Yahoo! and MSN adopt Overture, but mechanism proves unstable. Advertisers constantly change bids to avoid paying more than necessary. 2002: Google modifies keyword auction to have advertisers pay minimum amount necessary to maintain their position (GSP) - followed by Yahoo! and MSN.

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Keyword Auctions Basic model GSP auction

1 Keyword Auctions 2 Basic model 3 GSP auction

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Keyword Auctions Basic model GSP auction

A basic model: the setting

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Keyword Auctions Basic model GSP auction

A basic model: the setting

We consider an auction with n advertisers and n slots.

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Keyword Auctions Basic model GSP auction

A basic model: the setting

We consider an auction with n advertisers and n slots. Slots have associated fixed and public click-through-rates α1 ≥ α2 ≥ · · · ≥ αn.

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Keyword Auctions Basic model GSP auction

A basic model: the setting

We consider an auction with n advertisers and n slots. Slots have associated fixed and public click-through-rates α1 ≥ α2 ≥ · · · ≥ αn. By setting some of them = 0, the case with k < n slots is included.

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Keyword Auctions Basic model GSP auction

A basic model: the setting

We consider an auction with n advertisers and n slots. Slots have associated fixed and public click-through-rates α1 ≥ α2 ≥ · · · ≥ αn. By setting some of them = 0, the case with k < n slots is included. Advertiser i submits a bid bi, the amount he is willing to pay for a click.

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Keyword Auctions Basic model GSP auction

A basic model: outcome

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Keyword Auctions Basic model GSP auction

A basic model: outcome

An outcome is an assignment of advertisers to slots and of payments per click.

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Keyword Auctions Basic model GSP auction

A basic model: outcome

An outcome is an assignment of advertisers to slots and of payments per click. An assignment can be model as a permutation π. π(j) is the advertiser assigned to slot j.

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Keyword Auctions Basic model GSP auction

A basic model: outcome

An outcome is an assignment of advertisers to slots and of payments per click. An assignment can be model as a permutation π. π(j) is the advertiser assigned to slot j. A payment vector p, where pi is the price per click for advertiser i.

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Keyword Auctions Basic model GSP auction

A basic model: outcome

An outcome is an assignment of advertisers to slots and of payments per click. An assignment can be model as a permutation π. π(j) is the advertiser assigned to slot j. A payment vector p, where pi is the price per click for advertiser i. The benefit per click is assumed to be independent of the slot.

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Keyword Auctions Basic model GSP auction

A basic model: parameters

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Keyword Auctions Basic model GSP auction

A basic model: parameters

Each advertiser i has a private value vi, his value per click. The sequence v = (v1, ..., vn) is the valuation profile.

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Keyword Auctions Basic model GSP auction

A basic model: parameters

Each advertiser i has a private value vi, his value per click. The sequence v = (v1, ..., vn) is the valuation profile. Each advertiser i has a quality factor γi that reflects the clickability of its ad.

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Keyword Auctions Basic model GSP auction

A basic model: parameters

Each advertiser i has a private value vi, his value per click. The sequence v = (v1, ..., vn) is the valuation profile. Each advertiser i has a quality factor γi that reflects the clickability of its ad. In the simplest model γi = 1.

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Keyword Auctions Basic model GSP auction

A basic model: utilities

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Keyword Auctions Basic model GSP auction

A basic model: utilities

When advertiser i is assigned to the j-th slot, she gets αjγi clicks.

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Keyword Auctions Basic model GSP auction

A basic model: utilities

When advertiser i is assigned to the j-th slot, she gets αjγi clicks. If advertiser i is assigned to slot j at a price of pi per click then her utility is ui = αjγi(vi − pi), which is the number of clicks received times profit per click.

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Keyword Auctions Basic model GSP auction

A basic model: welfare

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Keyword Auctions Basic model GSP auction

A basic model: welfare

The social welfare of an outcome π is the total value of the solution for the participants, including the auctioneer.

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Keyword Auctions Basic model GSP auction

A basic model: welfare

The social welfare of an outcome π is the total value of the solution for the participants, including the auctioneer. SW (p, π, v, γ) =

n

  • i=1

απ−1(i)γi(vi − pi) +

n

  • j=1

αjγπ(j)pπ(j) =

n

  • j=1

αjγπ(j)vπ(j)

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Keyword Auctions Basic model GSP auction

A basic model: welfare

The social welfare of an outcome π is the total value of the solution for the participants, including the auctioneer. SW (p, π, v, γ) =

n

  • i=1

απ−1(i)γi(vi − pi) +

n

  • j=1

αjγπ(j)pπ(j) =

n

  • j=1

αjγπ(j)vπ(j) The social welfare is independent of the payments and the bids! SW (π, v, γ)

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Keyword Auctions Basic model GSP auction

VCR mechanism

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Keyword Auctions Basic model GSP auction

VCR mechanism

The optimal social welfare is Opt(v, γ) = max

π

SW (π, v, γ).

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Keyword Auctions Basic model GSP auction

VCR mechanism

The optimal social welfare is Opt(v, γ) = max

π

SW (π, v, γ). The efficient outcome sorts advertisers by their effective values γivi, and assigns them to slots in this order.

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Keyword Auctions Basic model GSP auction

VCR mechanism

The optimal social welfare is Opt(v, γ) = max

π

SW (π, v, γ). The efficient outcome sorts advertisers by their effective values γivi, and assigns them to slots in this order. We can design the associated VGC mechanism in which truthfulness is a dominant strategy.

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Keyword Auctions Basic model GSP auction

VCR mechanism

The optimal social welfare is Opt(v, γ) = max

π

SW (π, v, γ). The efficient outcome sorts advertisers by their effective values γivi, and assigns them to slots in this order. We can design the associated VGC mechanism in which truthfulness is a dominant strategy. Exercise: what would be the prices in the VCG auction?

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Keyword Auctions Basic model GSP auction

1 Keyword Auctions 2 Basic model 3 GSP auction

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Keyword Auctions Basic model GSP auction

GSP: Generalized Second Price Auction

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Keyword Auctions Basic model GSP auction

GSP: Generalized Second Price Auction

Players are asked to submit a bid, which is his reported valuation.

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Keyword Auctions Basic model GSP auction

GSP: Generalized Second Price Auction

Players are asked to submit a bid, which is his reported valuation. Given a bid profile b, we define the effective bid of advertiser i to be γibi

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Keyword Auctions Basic model GSP auction

GSP: Generalized Second Price Auction

Players are asked to submit a bid, which is his reported valuation. Given a bid profile b, we define the effective bid of advertiser i to be γibi which is her bid modified by her quality factor, analogous to the effective value defined above.

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Keyword Auctions Basic model GSP auction

GSP: Generalized Second Price Auction

Players are asked to submit a bid, which is his reported valuation. Given a bid profile b, we define the effective bid of advertiser i to be γibi which is her bid modified by her quality factor, analogous to the effective value defined above. The auctioneer sets π(k) to be the advertiser with the kth highest effective bid (breaking ties arbitrarily).

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Keyword Auctions Basic model GSP auction

GSP: Generalized Second Price Auction

Players are asked to submit a bid, which is his reported valuation. Given a bid profile b, we define the effective bid of advertiser i to be γibi which is her bid modified by her quality factor, analogous to the effective value defined above. The auctioneer sets π(k) to be the advertiser with the kth highest effective bid (breaking ties arbitrarily). That is, the GSP mechanism assigns slots with higher click-through-rate to advertisers with higher effective bids.

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Keyword Auctions Basic model GSP auction

GSP:pricing

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Keyword Auctions Basic model GSP auction

GSP:pricing

Prices per click are set as the smallest bid that guarantees the advertiser the same slot.

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Keyword Auctions Basic model GSP auction

GSP:pricing

Prices per click are set as the smallest bid that guarantees the advertiser the same slot. When advertiser i is assigned to slot k (that is, when π(k) = i), this critical value is defined as pi = γπ(k+1) γi bπ(k+1). where we take bn+1 = 0.

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Keyword Auctions Basic model GSP auction

GSP:pricing

Prices per click are set as the smallest bid that guarantees the advertiser the same slot. When advertiser i is assigned to slot k (that is, when π(k) = i), this critical value is defined as pi = γπ(k+1) γi bπ(k+1). where we take bn+1 = 0. In the case γi = 1, for each i, pi = bπ(k+1).

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Keyword Auctions Basic model GSP auction

GSP:utility

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Keyword Auctions Basic model GSP auction

GSP:utility

ui(b, γ) is the utility derived by advertiser i from the GSP mechanism when advertisers bid according to b: ui(b, γ) =απ−1(i)γi(vi − pi) = απ−1(i)[γivi − γπ(π−1(i)+1)bπ(π−1(i)+1)].

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Keyword Auctions Basic model GSP auction

GSP: Truthful bidding?

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Keyword Auctions Basic model GSP auction

GSP: Truthful bidding?

Consider a simple scenario.

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Keyword Auctions Basic model GSP auction

GSP: Truthful bidding?

Consider a simple scenario. Two slots positions, with α1 = 200 and α2 = 100. All γi = 1

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Keyword Auctions Basic model GSP auction

GSP: Truthful bidding?

Consider a simple scenario. Two slots positions, with α1 = 200 and α2 = 100. All γi = 1 Consider a bidder with value 10

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Keyword Auctions Basic model GSP auction

GSP: Truthful bidding?

Consider a simple scenario. Two slots positions, with α1 = 200 and α2 = 100. All γi = 1 Consider a bidder with value 10 Facing competing bids of 4 and 8.

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Keyword Auctions Basic model GSP auction

GSP: Truthful bidding?

Consider a simple scenario. Two slots positions, with α1 = 200 and α2 = 100. All γi = 1 Consider a bidder with value 10 Facing competing bids of 4 and 8.

Bidding 10 wins top slot, pay 8: profit 200 2 = 400. Bidding 5 wins next slot, pay 4: profit 100 6 = 600.

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Keyword Auctions Basic model GSP auction

GSP: Truthful bidding?

Consider a simple scenario. Two slots positions, with α1 = 200 and α2 = 100. All γi = 1 Consider a bidder with value 10 Facing competing bids of 4 and 8.

Bidding 10 wins top slot, pay 8: profit 200 2 = 400. Bidding 5 wins next slot, pay 4: profit 100 6 = 600.

If competing bids are 6 and 8, better to bid 10. . .

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Keyword Auctions Basic model GSP auction

GSP: Truthful bidding?

Consider a simple scenario. Two slots positions, with α1 = 200 and α2 = 100. All γi = 1 Consider a bidder with value 10 Facing competing bids of 4 and 8.

Bidding 10 wins top slot, pay 8: profit 200 2 = 400. Bidding 5 wins next slot, pay 4: profit 100 6 = 600.

If competing bids are 6 and 8, better to bid 10. . . It is not a dominant strategy to bid “truthfully”

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Keyword Auctions Basic model GSP auction

GSP: Nash equilibrium

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Keyword Auctions Basic model GSP auction

GSP: Nash equilibrium

A NE is a profile of bids b1 ≥ b2 ≥, . . . , ≥ bn such that,if π is the allocation of the GSP,

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Keyword Auctions Basic model GSP auction

GSP: Nash equilibrium

A NE is a profile of bids b1 ≥ b2 ≥, . . . , ≥ bn such that,if π is the allocation of the GSP, for any player j, for k < j, αj(γπ(j)vπ(j) − γπ(j+1)bπ(j+1)) ≥ αk(γπ(j)vπ(j) − γπ(k)bπ(k)) and, for k ≥ j, αj(γπ(j)vπ(j)−γπ(j+1)bπ(j+1)) ≥ αk(γπ(j)vπ(j)−γπ(k+1)bπ(k+1))

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Keyword Auctions Basic model GSP auction

GSP: Nash equilibrium

A NE is a profile of bids b1 ≥ b2 ≥, . . . , ≥ bn such that,if π is the allocation of the GSP, for any player j, for k < j, αj(γπ(j)vπ(j) − γπ(j+1)bπ(j+1)) ≥ αk(γπ(j)vπ(j) − γπ(k)bπ(k)) and, for k ≥ j, αj(γπ(j)vπ(j)−γπ(j+1)bπ(j+1)) ≥ αk(γπ(j)vπ(j)−γπ(k+1)bπ(k+1)) A player decreasing his bid can acquire a lower slot paying the price the player in this slot is paying.

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Keyword Auctions Basic model GSP auction

GSP: Nash equilibrium

A NE is a profile of bids b1 ≥ b2 ≥, . . . , ≥ bn such that,if π is the allocation of the GSP, for any player j, for k < j, αj(γπ(j)vπ(j) − γπ(j+1)bπ(j+1)) ≥ αk(γπ(j)vπ(j) − γπ(k)bπ(k)) and, for k ≥ j, αj(γπ(j)vπ(j)−γπ(j+1)bπ(j+1)) ≥ αk(γπ(j)vπ(j)−γπ(k+1)bπ(k+1)) A player decreasing his bid can acquire a lower slot paying the price the player in this slot is paying. A player increasing his bid can only acquire a higher slot paying not the price the player in this slot is paying but its bid.

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Keyword Auctions Basic model GSP auction

GSP: Nash equilibrium

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Keyword Auctions Basic model GSP auction

GSP: Nash equilibrium

The NE equation have in general more than one solution, so there are many NE.

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Keyword Auctions Basic model GSP auction

GSP: Nash equilibrium

The NE equation have in general more than one solution, so there are many NE. We have also a social welfare. PoS? PoA?

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Keyword Auctions Basic model GSP auction

GSP: Nash equilibrium

The NE equation have in general more than one solution, so there are many NE. We have also a social welfare. PoS? PoA? Among the NE are there some with nice properties?

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Keyword Auctions Basic model GSP auction

GSP: Nash equilibrium

The NE equation have in general more than one solution, so there are many NE. We have also a social welfare. PoS? PoA? Among the NE are there some with nice properties? Is there an efficient NE?

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Keyword Auctions Basic model GSP auction

GSP: Envy-free equilibrium

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Keyword Auctions Basic model GSP auction

GSP: Envy-free equilibrium

Definition Given a GSP with n players defined by click-through-rates α1 ≥ α2 ≥ · · · ≥ αn, quality scores γ1 ≥ γ2 ≥ · · · ≥ γn and valuations v1, . . . , vn. A bid vector b is an envy-free equilibrium if, for any pair j, k of players, player j would not prefer player k’s allocation and payments rather than their own. Formally αj(γπ(j)vπ(j) − γπ(j+1)bπ(j+1)) ≥ αk(γπ(j)vπ(j) − γπ(k+1)bπ(k+1)) where π(j) is the allocation of the GSP auction.

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Keyword Auctions Basic model GSP auction

GSP: Envy-free equilibrium

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Keyword Auctions Basic model GSP auction

GSP: Envy-free equilibrium

Every envy-free equilibrium is a NE

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Keyword Auctions Basic model GSP auction

GSP: Envy-free equilibrium

Every envy-free equilibrium is a NE Conditions in k ≥ j are the same and, for k < j te conditions are stricter.

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Keyword Auctions Basic model GSP auction

GSP: Envy-free equilibrium

Every envy-free equilibrium is a NE Conditions in k ≥ j are the same and, for k < j te conditions are stricter. Every envy-free equilibrium is efficient (exercise)

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Keyword Auctions Basic model GSP auction

GSP: Envy-free equilibrium

Every envy-free equilibrium is a NE Conditions in k ≥ j are the same and, for k < j te conditions are stricter. Every envy-free equilibrium is efficient (exercise) Are there envy-free equilibria?

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Keyword Auctions Basic model GSP auction

GSP: Envy-free equilibrium

Every envy-free equilibrium is a NE Conditions in k ≥ j are the same and, for k < j te conditions are stricter. Every envy-free equilibrium is efficient (exercise) Are there envy-free equilibria? Sort bidders so that γ1v1 ≥ · · · ≥ γnvn. Consider the bid vector b,

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Keyword Auctions Basic model GSP auction

GSP: Envy-free equilibrium

Every envy-free equilibrium is a NE Conditions in k ≥ j are the same and, for k < j te conditions are stricter. Every envy-free equilibrium is efficient (exercise) Are there envy-free equilibria? Sort bidders so that γ1v1 ≥ · · · ≥ γnvn. Consider the bid vector b, b1 = v1 and, for i = j

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Keyword Auctions Basic model GSP auction

GSP: Envy-free equilibrium

Every envy-free equilibrium is a NE Conditions in k ≥ j are the same and, for k < j te conditions are stricter. Every envy-free equilibrium is efficient (exercise) Are there envy-free equilibria? Sort bidders so that γ1v1 ≥ · · · ≥ γnvn. Consider the bid vector b, b1 = v1 and, for i = j bi = 1 αi−1γi  

j=i

n(αj−1 − αj)γjvj  

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Keyword Auctions Basic model GSP auction

GSP: Envy-free equilibrium

Every envy-free equilibrium is a NE Conditions in k ≥ j are the same and, for k < j te conditions are stricter. Every envy-free equilibrium is efficient (exercise) Are there envy-free equilibria? Sort bidders so that γ1v1 ≥ · · · ≥ γnvn. Consider the bid vector b, b1 = v1 and, for i = j bi = 1 αi−1γi  

j=i

n(αj−1 − αj)γjvj   This is a envy-free equilibrium!

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Keyword Auctions Basic model GSP auction

NE efficiency?

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Keyword Auctions Basic model GSP auction

NE efficiency?

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Keyword Auctions Basic model GSP auction

NE efficiency?

Are alll NE efficent?

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Keyword Auctions Basic model GSP auction

NE efficiency?

Are alll NE efficent? Take 1 2 α 1 1/2 v 1 1/2 γ 1 1 b 1/2

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Keyword Auctions Basic model GSP auction

NE efficiency?

Are alll NE efficent? Take 1 2 α 1 1/2 v 1 1/2 γ 1 1 b 1/2 b is a NE and its efficiency is 1 1

2 + 1 21 = 1.

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Keyword Auctions Basic model GSP auction

NE efficiency?

Are alll NE efficent? Take 1 2 α 1 1/2 v 1 1/2 γ 1 1 b 1/2 b is a NE and its efficiency is 1 1

2 + 1 21 = 1.

The optimal allocation has efficiency 1 1 + 1

2 1 2 = 5/4

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Keyword Auctions Basic model GSP auction

NE efficiency?

Are alll NE efficent? Take 1 2 α 1 1/2 v 1 1/2 γ 1 1 b 1/2 b is a NE and its efficiency is 1 1

2 + 1 21 = 1.

The optimal allocation has efficiency 1 1 + 1

2 1 2 = 5/4

PoA?

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Keyword Auctions Basic model GSP auction

PoA

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Keyword Auctions Basic model GSP auction

PoA

In the full information setting the quality factors γ are fixed and common knowledge.

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Keyword Auctions Basic model GSP auction

PoA

In the full information setting the quality factors γ are fixed and common knowledge. Theorem The (pure) PoA of GSP in the full information setting is at most the golden ratio 1

2(1 +

√ 5) ≈ 1.618

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Keyword Auctions Basic model GSP auction

PoA

In the full information setting the quality factors γ are fixed and common knowledge. Theorem The (pure) PoA of GSP in the full information setting is at most the golden ratio 1

2(1 +

√ 5) ≈ 1.618 and at least 1.282 .

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SLIDE 95

Keyword Auctions Basic model GSP auction

Design directions

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SLIDE 96

Keyword Auctions Basic model GSP auction

Design directions

Main focus in the extension of keyword auctions to other settings.

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SLIDE 97

Keyword Auctions Basic model GSP auction

Design directions

Main focus in the extension of keyword auctions to other settings. Goal: Design mechanisms that verify properties. For example:

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SLIDE 98

Keyword Auctions Basic model GSP auction

Design directions

Main focus in the extension of keyword auctions to other settings. Goal: Design mechanisms that verify properties. For example: Individual Rationality: Each player has net non-negative utility from participating in the auction, i.e., ui ≥ 0.

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SLIDE 99

Keyword Auctions Basic model GSP auction

Design directions

Main focus in the extension of keyword auctions to other settings. Goal: Design mechanisms that verify properties. For example: Individual Rationality: Each player has net non-negative utility from participating in the auction, i.e., ui ≥ 0. Incentive compatibility (a.k.a. truthfulness): It is a dominant strategy for each player to participate in the auction and report their true value.

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slide-100
SLIDE 100

Keyword Auctions Basic model GSP auction

Design directions

Main focus in the extension of keyword auctions to other settings. Goal: Design mechanisms that verify properties. For example: Individual Rationality: Each player has net non-negative utility from participating in the auction, i.e., ui ≥ 0. Incentive compatibility (a.k.a. truthfulness): It is a dominant strategy for each player to participate in the auction and report their true value. Pareto-optimality: An allocation π and payments p is Pareto-optimal if and only if there is no alternative allocation and payments where all players’ utilities and the revenue of the auctioneer do not decrease, and at least one of them increases.

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