Auction Markets Jon Levin Winter 2010 Economics 136

Auction Markets

Jon Levin

Winter 2010

Economics 136

Multi-Unit Auctions

Examples

Treasury auctions Auction-rate securities IPO auctions Privatization Electricity markets Asset sales Condominium sales Wine/Art/Antiques Auto auctions

Natural resources Radio spectrum Emissions permits Airport landing slots Bus routes Procurement contracts Sponsored search Internet display ads eBay marketplace

Sequential auctions

Auction houses often sell identical goods sequentially (e.g. lots of wine).

What happens at sequential auctions? Should you bid your value in the first auction? Are early prices higher or lower than later prices?

Sotheby Wine Auctions

Source: Ashenfelter (1989, Journal of Economic Perspectives)

Declining Prices

A puzzle?

Standard theory: in a symmetric private value setting, prices need not be equal across sequential first or second-price auctions, but…

Weber’s Theorem. Equilibrium prices should follow a random walk: E[pt+1|p1…pt]=pt

Yet the “declining price anomaly appears to be quite robust – wine, art, cattle, etc – and variants observed with non-identical items.

This remains something of an open puzzle.

Simultaneous Sales of Identical items

Consider auction for k identical items.

Possible “one-shot” auction methods

“Uniform price” (clock and sealed bid)

“Discriminatory price” (pay-your-bid and Vickrey).

We will see that one important issue is whether

bidders want just one item, or are potentially interested

in winning several items.

“Uniform price” auctions

Sellers often want to run an auction in which all winners pay the same “uniform” price. Perceived as “fair”; achieves “price discovery”

Uniform price formats Clock auction: seller announces a sequence of prices and

bidders name quantities until a market-clearing price is found and auction ends.

Sealed bidding: participants bid a price-quantity schedule and bids are used to determine the uniform market-clearing price.

British CO2 Auctions

Greenhouse Gas Emissions Trading Scheme Auction, United Kingdom, 2002.

UK government aimed to spend 215 million British pounds to get firms reduce CO2 emissions.

Clock auction used to determine What price to pay per unit? Which firms to reward?

Greenhouse Auction Rules Auctioneer calls out price

Price starts high and decreases each round.

Each round, bidders state tons of CO2 they will abate

Tons abated can only decrease as prices decrease.

Auctioneer multiplies tons of abatement times price. If total cost exceeds budget, lowers the price When total cost first falls short of budget, auction ends and

that allocation is implemented

Auction results

38 bidders (34 winners), 4m metric tons of CO2 reduction.

Price per metric ton: £215m/4m= £53.75

Graphical treatment

Q

P UK “Demand Curve, defined so that Q*P(Q)=£215m

p1

p2

p*

Falling pricestrace out a “supply curve”.

Sealed bid version

Uniform-price sealed bid auction Auctioneer posts its demand curve

Bidders submit “supply curves” - i.e. how much they will supply at each price.

Individual supply curves are aggregated to form an aggregate supply curve.

Price is set so that supply = demand.

Strategic equivalence? Are clock and sealed auctions strategically equivalent?

Suppose bidders in the clock auction observe only the prices and that prices decline in a fixed sequence.

Bidders are then effectively being asked to reveal their supply curves from the top down, with no new information each round other than that the current price is relevant.

So yes, the clock auction is strategically equivalent to a sealed bid auction in which supply curves get written down in advance.

Equivalence may fail if more information is revealed each round.

Incentives with Uniform Price

Suppose each bidder wants a single item. Values are drawn from U[0,1]. n bidders, k items with n>k. Bidders submit bids: price = k+1 highest bid.

Theorem. For a bidder with single item demand, it is a dominant strategy to bid one’s value. Proof. Similar to the second price case.

Demand reduction Example: three items for sale

Bidder 1: value 120 and wants 1 item. Bidder 2: value 110 and wants 1 item. Bidder 3: value 100 and wants 1 item. Bidder 4: value 105 and wants 2 items.

Consider what happens with “truthful” bidding Bids are 120, 110, 105, 105, 100. Three highest bids are winners Fourth highest bid is 105 => winners pay 105 each.



“Demand reduction” by bidder 4 If he bids 105, he wins 1 item and pays 105. If he bids 101, bids are 120, 110, 101, 101, 100. He still wins 1 and lowers the price to 101!

Example, cont.

Again, three items and values Bidder 1: 120

Bidder 2: 110

Bidder 3: 100

Bidder 4: 115 and wants two units.

Demand reduction by bidder 4 Bid 115 for both units => wins two, price =110.

Bid 115 for first unit, 100 for second => wins 1, p=100.

Bidder four optimally exercises “market power”.

Demand Reduction Picture

Q

Pb1

SupplyQ=3

3

b2

b3

b4

Opponent Bidsand demand curve

“Residual supply curve”

Multi-unit bidder wants tomaximize profit by behavingas a monopsonist against theresidual supply curve.

Low Price Equilibrium

Q

P Supply

3

“Residual supply curve”in a “regular” equilbriumResidual supply curve in alow price equilibrium

Residual supply curve if seller “adds elasticity”

Expanded supply

Multi-Unit Auctions and Financial Assets

Today’s Lecture

Uniform price sealed bid auctions Virtues: simple, “fair”, reveal “market price” Concerns: demand reduction, “low price” eqm

Comparison to alternatives Discriminatory price auctions Vickrey auction

Application to financial markets Extensions to multiple goods

Uniform-price sealed bid auction

Auctioneer posts its supply curve

Bidders submit “demand curves” - i.e. how much they want at each price.

Individual demand curves are aggregated to form an aggregate demand curve.

Price is set so that supply = demand

Demands at the market clearing price are satisfied.

Incentives with Uniform Price N bidders, K items with N>K Each bidder wants one unit, values U[0,1]. Bids submitted (offer to buy one unit at some price) Market clearing price = any price between the kth highest bid and

the K+1th highest bid (why?) Assume lowest clearing price: K+1 highest bid.

Theorem. For a bidder with single item demand, it is a dominant strategy to bid one’s value. Proof. Similar to the second price case.

Theorem is not true if bidders want multiple units (next slide!)



Consider what happens with “truthful” bidding Bids are 120, 110, 105, 105, 100. Three highest bids are winners Fourth highest bid is 105 => winners pay 105 each.



“Demand reduction” by bidder 4 If he bids 105, he wins 1 item and pays 105. If he bids 101, bids are 120, 110, 101, 101, 100. He still wins 1 and lowers the price to 101!

Example, cont.

Again, three items and values Bidder 1: 120

Bidder 2: 110

Bidder 3: 100

Bidder 4: 115 and wants two units.

Demand reduction by bidder 4 Bid 115 for both units => wins two, price =110.

Bid 115 for first unit, 100 for second => wins 1, p=100.

Bidder four optimally exercises “market power”.

Demand Reduction

General model N bidders, K items, where 2k<N. Each bidder has positive value for at least two items. Bidder values random, but always satisfy v1j ≥ v2j

Theorem. In the k+1 price auction, it is weakly dominant to bid true value for first unit. However: there is no equilibrium in which bidders all bid their full

values for both items, and there is no equilibrium in undominated strategies that is

efficient for all realized valuations.

“Low price” Equilibria

With fixed supply, uniform price auction can have equilibria with low prices due to demand reduction.

Example: three units, three bidders. Bidders value units at 10, want as many as possible. The price “should be” 10 if there is competition. What if each bidder offers to buy one unit for 10, and no

additional units at any price above zero. Bidders split the units, price is zero! Because a bidder who wants to purchase additional units

has to pay ten, there is no reason to demand more. The low price bidding is a Nash equilibrium!

Making supply elastic Suppose the seller offers

To sell 3 units at any price To sell 4 units if (and only if) price exceeds 4

Claim: Any Nash equilibrium for bidders involves selling four units at a price of at least 4. If bidders bid (10,0), each bidder gets 1 unit, p=0. Each bidder has incentive to bid (10,4) => win two units

and price increases to four. Profit of 2*(10-4)=12>10. Equilibrium will have one bidder winning two items, and

fifth highest bid somewhere between 4 and 10. Somewhat surprisingly, seller has managed to

increase supply and yet also increase prices.

California electricity crisis The California electricity crisis of 2001

Prices go from around $45 megawatt-hour to as high as $1400. Paul Joskow of MIT: “California electricity crisis is what happens

when a vertical supply curve intersects a vertical demand curve.” Steep supply/demand: during the crisis a 5% lowering of demand

(or increase in supply) would have lowered prices by 50%! Borenstein, Bushnell, Wolak (AER, 2003): vertical demand

because consumers don’t react to price, vertical supply because generators strategically withhold power.

Remedies? Create elasticity in electricity demand (how?). Restrict slope of submitted supply curves. Encourage build-out of additional capacity (how?). Forward contracts (unravel the market!).

Increasing Returns… Discussion implicitly focused on bidders with

decreasing marginal values who submit downward-sloping demand curves.

What if there are scale economies? Two units for sale Bidder 1 offers 10 for one unit. Bidder 2 offers 5 for first unit and 11 for second. There is no uniform price that clears the market!

Not much is known about performance of uniform price auctions where there are scale economies.

Expanding the example… Two units for sale

Bidder 1 offers 10 for one unit. Bidder 2 offers 5 for first unit and 11 for second.

Consider possible prices At p < 8, demand = 3 At p = 8, demand = 1 or 3 At p in (8,10), demand = 1 At p = 10, demand = 0 or 1 At p > 10, demand = 0

Problem: demand “crosses” supply at price = 8, but at that price, Bidder 1 demands 1, and Bidder 2 demands 0 or 2 but is unwilling to buy 1! So can’t have demand=supply!!!

Discriminatory Price Auctions

Alternative is a “pay-your-bid” format Bidders submit bids (offers to buy different

quantities at different prices) Seller finds price where supply=demand All bids above clearing price are satisfied, but

winners pay their bid rather than the clearing price.

Example Example: three items for sale


Suppose “truthful bids” Bidder 1: (1, 120) “buy one at any price < 120” Bidder 2: (1, 110) Bidder 3: (1, 100) Bidder 4: (2, 105)

Outcome: 1, 2, 4 win and pay 120, 110, 105. Is this an equilibrium? Why or why not?

Example, cont. Example

Bidders 1, 2, 3 want 1 item and values 120, 110, 100. Bidder 4: wants two items and value 105.

Possible equilibrium bids? Bidder 1: (1, 105) Bidder 2: (1, 105) Bidder 3: (1, 100) Bidder 4: (2, 105)

So 1, 2, 4 win and all pay 105. Is this an eqm? Why or why not?

Example, cont. Example

Bidders 1, 2, 3 want 1 item and values 120, 110, 100. Bidder 4: wants two items and value 105.

Possible equilibrium bids? Bidder 1: (1, 100 + penny) Bidder 2: (1, 100 + penny) Bidder 3: (1, 100) Bidder 4: (2, 100 + penny)

So 1, 2, 4 win and all pay 100 + penny. Is this an eqm?

The actual equilibrium involves mixed strategies with bids distributed between 100 and 105!

Uniform vs. Discriminatory

Both auctions can be inefficient. Both auctions create an incentive to “reduce demand” if

bidders want multiple units.

Does one lead to higher prices? Not clear in general.

Does one lead to higher or lower participation or reveal more useful information? Sometimes argued that uniform price auction is good for

small bidders b/c its easy to participate and get the “market price”, but discriminatory price can sometimes be painful for large high-value bidder.

US Treasury Experience US Treasuy historically ran discriminatory auctions

(since the 1970s) to sell bonds. Beginning in 1992, switched to uniform price. Rationale

Aim for more liquid market (transparency) Encourage broader participation Encourage competition (slightly vague)

Features of the market: large, highly liquid There is some “price impact” from the new issuance. There is also a “when-issued” market that runs prior to the

auction, so participants can guage likely price. Many participants (75-85 bidders), but relatively small

number of primary dealers win a lot of the bonds.

Treasury experience, cont.

Evidence from US transition Switch to uniform price led to somewhat lower spread

between auction price and WI price (but not very large or stat. significant).

Somewhat more volatility between auction price and WI price b/c more dispersed bids w/ uniform price auction.

Awards to primary dealers similar under the two types of auctions, but share of awards to the very top dealers decreased with uniform price.

Debate in other countries: possible that design may matter more if market is thinner or less transparent.

TARP Warrant Auctions

As part of TARP, Treasury received warrants from banks that were “bailed out” Warrants give holder a right to buy the stock at some

“strike price” at any point over the next 10 years. Like an option except that when a warrant is exercised, the

firm issues new shares rather than buying back shares (so there is dilution)

Treasury negotiated with banks to sell them back the warrants but some negotiations failed, leaving treasury to dispose of the warrants.

Question: how to design an auction to sell the warrants?

Warrant auctions, cont. Questions one must address

Uniform price or discriminatory? Sell all warrants at once, or over time? Sealed bid or ascending auction? Potential for a “winners curse”

Treasury (via auction agent) decided on a standard treasury format, ran three in fall. Evidence from JPM auction (largest at $1 bn) suggests a

large price impact (auction price 30% below subsequent after-market price.

Now treasury must consider whether this was a big number, and whether to change the design. What data would you want to look at?

An Efficient Auction?

Back to our example with three items for sale Bidder 1: value 120 and wants 1 item. Bidder 2: value 110 and wants 1 item. Bidder 3: value 100 and wants 1 item. Bidder 4: value 105 and wants 2 items.

Is there a pricing rule that would make it a dominant strategy for each bidder to bid truthfully – and would lead to an efficient allocation of the items?

“Vickrey” Prices

Set price for each bidder equal to the value per unit the bidder “displaces. Equivalently: use submitted values to compute total value

with and without the bidder present.

Set price for the bidder so that his profit equals the value he creates.

Vickrey pricing makes bidding truthfully a dominant strategy.

But Vickrey prices are not uniform prices!

Vickrey pricing

Example: three items for sale Bidder 1: value 120 and wants 1 item. Bidder 2: value 110 and wants 1 item. Bidder 3: value 100 and wants 1 item. Bidder 4: value 105 and wants 2 items.

Vickrey pricing if truthful bids Bidders 1 and 2 win, pay 105 each (displace 4). Bidder 4 wins one unit, pays 100 (displaces 3).

Vickrey pricing, again

Example: three items for sale Bidder 1: value 120 and wants 1 item. Bidder 2: value 110 and wants 1 item. Bidder 3: value 100 and wants 1 item. Bidder 4: value 115 and wants 2 items.

Vickrey pricing if truthful bids Bidder 1 wins and pays 110 (displaces bidder 2). Bidder 4 wins two units, pays 100 for first unit (displaces

bidder 3) and 110 for second (displaces bidder 2).

General Lessons Uniform price auctions have fairness, transparency virtues

But encourage demand reduction when bidders want multiple units

Also create the possibility of low price “collusive seeming” equilibria (making supply elastic can help with this problem).

Discriminatory price auctions also encourage demand reduction, but sometimes viewed as a way to raise revenue from high value bidders – although revenue implications generally unclear.

Vickrey pricing can eliminate demand reduction and restore efficiency, but the uniform price property is lost.

Multi-Item Auctions and Matching

Multiple Kinds of Goods

Can we design successful auctions that allow for multiple kinds of goods? Spectrum licenses covering different cities. Electricity delivered from/to different places. Multiple kinds of financial assets. Emissions reductions in different years. Different kinds of sponsored search placements.

General issues

What would be desirable properties? Auction finds “market clearing” prices (uniform price)

Auction is strategyproof (Vickrey), or nearly so.

Auction is relatively simple, robust to collusion, etc.

The challenge Bidder preferences may be complex and complex

preferences are hard to state in sealed bid auction.

Complementarities (like increasing returns) may imply that market clearing prices don’t exist.

Auction complexity and strategy can be serious issues.

Connection to matching

There is a connection to matching theory… Treat bidders as one side of the market Treat items for sale as the other side We are interested in a matching (for now, one-to-

one, but potentially many-to-one). But now we have to determine prices as well as

the assignment.

Deferred acceptance?

Each bidder submits a preference list Example: first choice is to pay zero for item 1, second

choice is to pay $1 for item 1, third choice is to pay $0 for item 2, fourth choice is to pay $2 for item 1, etc..

Seller runs deferred acceptance algorithm Bidders “propose” to the items.

Items prefer to sell for more money, accept highest offer.

Algorithm will eventually terminate.

Auctions & Matching

Ascending auction(Kelso & Crawford, 1982)“Bids” made by computer.

1. Bidders offer most preferred remaining acceptable purchase.

2. Items hold best bid, reject others.

3. Rejected bidder strikes offer from his/her list.

4. Process continues until no new offers or rejections.

5. Implement last held allocation.

Matching algorithm(Gale & Shapley, 1962)Offers made by computer.

1. Doctors apply to most preferred remaining acceptable program.

2. Hospitals hold best doctor, reject others.

3. Rejected doctor strikes the hospital from his/her list.

4. Process continues until no new offers or rejections.

5. Implement last held allocation.

Deferred acceptance “auction” What we know from matching theory

Suppose bidders are each interested in a single item.

Algorithm will converge to a “stable” allocation.

Bidder-offering auction is strategy-proof for the bidders.

Connection to auctions/markets Stability: at the deferred acceptance final price for each item,

there is exactly one bidder, so supply = demand!

A stable allocation is a competitive equilibrium

Strategy-proof: the competitive equilibrium prices are the same as one would get from a Vickrey auction!

Extension to multi-good demand?

Sponsored Search Auctions

Sponsored Search Auctions

Google revenue in 2008: $21,795,550,000.

Hal Varian, Google chief economist: “What most people don’t realize is that all that money

comes pennies at a time.”

Today we’ll discuss internet keyword auctions. References: Varian 2008, Edelman et al. 2007.

Keyword Auctions

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 in order of bid (more on this later). Advertisers pay bid of the advertiser in the position below. “Generalized second price” auction format.

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

Brief History of Sponsored Search Auctions

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 (i.e. GSP)- followed by Yahoo! and MSN.

Example Two positions: receive 200 and 100 clicks per day Advertisers 1,2,3 have per-click values $10, $4, $2.

Efficient allocation Advertiser 1 gets top slot: value created 200*10 = 2000 Advertiser 2 gets 2nd slot: value created 100*4 = 400

Total value creation: $2400

Example: competitive eqm Two positions: receive 200 and 100 clicks per day Advertisers 1,2,3 have per-click values $10, $4, $2.

Competitive equilibrium Set prices for slots (p1, p2) so that demand = suppy

Example: p2 = 2 and p1 = 4 Advertiser 3 demands nothing Advertiser 2 demands slot 2: 100*(4-2)>200*(4-4)=0 Advertiser 1 demands slot 1: 200*(10-4)>100*(10-2)

Efficient outcome with revenue: $800+$200= $1000

Example: competitive eqm Two positions: receive 200 and 100 clicks per day Advertisers 1,2,3 have per-click values $10, $4, $2.

Many possible mkt-clearing prices (p1, p2) Advertiser 3 must demand nothing, so p1, p2 2 Advertiser 2 must demand slot 2, so

p2 4, and 2p1- p2 4 (so that 200*(4- p1) < 100*(4-p2) )

Advertiser 1 must demand slot 1, so 2p1- p2 10 (so that 200*(10- p1) < 100*(10-p2) )

Allocation efficient with revenue: 200p1+100p2

Competitive Eqm

p2

p1

2 4

4

8

6

2

Possible competitive equilibrium prices!

Can we use an auction to “find”these prices?

Example: Pay-your-Bid Two positions: receive 200 and 100 clicks per day Advertisers 1,2,3 have per-click values $10, $4, $2.

Overture auction (pay your bid) Advertiser 3 will offer up to $2 per click Advertiser 2 has to bid $2.01 to get second slot Advertiser 1 wants to bid $2.02 to get top slot. But then advertiser 2 wants to top this, and so on.

Pay your bid auction is unstable!

Overture bid patterns

Edelman & Ostrovsky (2006): “sawtooth” pattern caused by auto-bidding programs.

Overture bid patterns, cont.

Vickrey Auction

Bidders submit bids (price per click) Auctioneer treats bids as values

Finds allocation that maximizes value created So high bid gets top slot, and so forth

Vickrey payment for bidder j Note that if bidder j gets a slot, he is “displacing” other

bidders by moving them down a slot. Compute the lost value from this displacement (e.g. if j

pushes k down a slot, k loses clicks that are worth some amount to k)

Bidder j’s payment equals total “displacement” cost, or equivalently the externality j imposes on other bidders.

Vickrey Auction, cont.

Second price auction is a Vickrey auction Winner “displaces” second highest bidder Winner pays the displaced value: 2nd high bid Also a Google auction with one click for sale!

General properties of Vickrey auction Dominant strategy to bid truthfully (bid = value)! Outcome is efficient (maximizes total value)!

Vickrey auction, aside

Recall our example with three items for sale Bidder 1: value 120 and wants 1 item. Bidder 2: value 110 and wants 1 item. Bidder 3: value 100 and wants 1 item. Bidder 4: value 105 and wants 2 items.

Vickrey pricing if truthful bids Bidders 1 and 2 win, pay 105 each (displace 4). Bidder 4 wins one unit, pays 100 (displaces 3).

Example: Vickrey auction

Two positions: receive 200 and 100 clicks per day Advertisers 1,2,3 have per-click values $10, $4, $2.

Vickrey auction Advertisers are submit bids, assigned efficiently given submitted

bids, and have to pay the value their ad displaces. Dominant strategy to bid one’s true value.

Vickrey outcome Advertiser 1 gets top, then 2, and 3 gets nothing. Adv. 2 pays $200 (displaces 3) for 100 clicks, or $2 /click. Adv. 1 pays $600 (displaces 3 & 2) for 200 clicks, $3 /click.

Efficient allocation with revenue of $800.

Deriving the Vickrey prices Two positions: receive 200 and 100 clicks per day Advertisers 1,2,3 have per-click values $10, $4, $2.

Vickrey payment for Bidder 2 Bidder 2 displaces 3 from slot 2 Value lost from displacing 3: $2 * 100 = $200 So Bidder 2 must pay $200 (for 100 clicks), or $2 per click.

Vickrey payment for Bidder 1 Displaces 3 from slot 2: must pay $200 Displaces 2 from slot 1 to 2: must pay $4*(200-100)=$400 So Bidder 1 must pay $600 (for 200 clicks), or $3 per click.

Vickrey “prices” are therefore p2 = 2 and p1 = 3, revenue $800.

Vickrey prices

p2

p1

2 4

4

8

6

2

Vickrey prices arethe lowest competitiveequilibrium prices!

Vickrey prices

Google “GSP” Auction

Generalized Second Price Auction Bidders submit bids (per click) Top bid gets slot 1, second bid gets slot 2, etc. Each bidder pays the bid of the bidder below him.

Do the bidders want to bid truthfully?

Truthful bidding?

Not a dominant strategy to bid “truthfully”! Two positions, with 200 and 100 clicks.

Consider bidder with value 10

Suppose competing bids are 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…

Example: GSP auction Two positions: receive 200 and 100 clicks per day Advertisers 1,2,3 have per-click values $10, $4, $2.

Generalized Second Price Auction In this case, it is an equilibrium to bid truthfully Bidder 2 gets slot 2 and pays $2 per click (or $200) Bidder 1 gets slot 1 and pays $4 per click (or $800)

Efficient allocation, revenue is $1000 (> Vickrey!)

Why an equilibrium? Bidder 3 would have to bid/pay $2 to get slot 2 – not worth it. Bidder 2 would have to bid/pay $10 to get slot 1 – not worth it. Bidder 1 could bid/pay $2 and get slot 2, but also not worth it.

GSP equilibrium prices

p2

p1

2 4

4

8

6

2

GSP prices are also competitive equilibrium prices!

Vickrey prices

GSP eqm

Not the only GSPequilibrium, however

Example: GSP auction Two positions: receive 200 and 100 clicks per day Advertisers 1,2,3 have per-click values $10, $4, $2.

Another GSP equilibrium (with Vickrey prices!) Bidder 3 bids $2 and gets nothing Bidder 2 bids $3 and pays $2 per click for slot 2 Bidder 1 bids $10 and pays $3 per click for slot 1

And another GSP equilibrium (w/ higher prices) Bidder 3 bids $3 and gets nothing Bidder 2 bids $5 and pays $3 per click for slot 2 Bidder 1 bids $6 and pays $5 per click for slot 1


p2

p1

2 4

4

8

6

2

GSP equilibrium prices are also competitive equilibrium prices!

Vickrey prices

GSP eqm

GSP eqm

General Model

K positions k=1,..,K N bidders i = 1,…,N

Bidder i values position k at uik = vn • xk

xk is quantity of clicks, x1>x2>…>xK

vn is value of a click, v1>v2>…>vK

Efficient allocation is assortative Bidder k should get slot k to max total value.

GSP Auction Rules

Each agent i submits bid bi

Interpret as “maximum amount i offers to pay per click”

Positions assigned in order of bids

Agent i’s price per click is set equal to the bid of agent in the next slot down.

Let bk denote kth highest value and vk value.

Payoff of kth highest bidder:

vk • xk – bk+1 • xk = (vk - bk+1) • xk

GSP equilibrium analysis

Full information Nash equilibrium NE means no bidder wants to change positions

Nash eqm is a bid profile b1,…, bK such that

(vk - bk+1) • xk (vk - bm+1) • xm for m>k

(vk - bk+1) • xk (vk - bm) • xm for m<k

Lots of Nash equilibria, including some that are inefficient…

Locally Envy-Free

Definition: An equilibrium is locally envy-free if no player can improve his payoff by exchanging bids with the player ranked one position above him. Motivation: “squeezing” – if an equilibrium is not

LEF, there might be an incentive to squeeze.

Add the constraint for all k

(vk - bk+1) • xk (vk - bk) • xk-1

Stable Assignments

Close connection between GSP equilibria / Competitive eqm / Stable assignments !

Think of bidders being “matched” to positions. Matching postion i to bidder k with price pk gives bidder payoff: (vi -pk)xk and position payoff pkxk

Stability: no bidder/position want to block. All stable assignments are efficient (assortative). Relevant blocks are bidders looking to move up or down

one position. (think about this).

Stable assignments At a stable assignment, matching is efficient. Each position k commands a price pk.

Prices that support a stable allocation satisfy:

(vk - pk) • xk (vk – pk-1) • xk-1

(vk - pk) • xk (vk – pk+1) • xk+1

These are the conditions for a competitive equilibria Essentially they say that bidder k demands position k So therefore at these prices, supply = demand!

Equivalence Result

Theorem: Outcome of any locally envy-free equilibrium of

the GSP is a stable assignment (i.e. competitive equilibrium allocation)

Provided that |N|>|K|, any stable assignment (i.e. competitive equilibrium allocation) is an outcome of a locally envy-free equilibrium.


p2

p1

2 4

4

8

6

2

The set of competitiveequilibrium prices corresponds to the setof GSP equilibrium prices!

Vickrey prices

GSP eqm

GSP eqm

Revenue and Prices

Theorem There exists a bidder-optimal competitive

equilibrium (equivalently, GSP equilibrium) and a seller-optimal one.

The bidder optimal competitive equilibrium is payoff-equivalent to the Vickrey outcome.

Corollary: any locally envy free GSP equilibrium generates at least as much revenue as Vickrey.

Internet Advertising Markets

Today’s Lecture

Sponsored Search Market Recap of last time Examples of GSP/Comp Eqm/Vickrey Auction design & platform competition

Display Advertising Market Structure and organization of the market Form of contracts, auctions vs prices Heterogeneity, targeting and conflation

Sponsored Search Recap

Search engines sell positions on results page Advertisers bid for keywords on per-click basis “Generalized second price” auction for each query

Simple model of auction setting shows that: Usually range of market clearing (per click) prices Vickrey auction leads to lowest mkt-clear. prices. Many possible GSP equilibrium outcomes, but the

payments coincide with mkt-clearing prices. Equivalence btwn mkt-clear prices, GSP outcomes and

stable matchings of advertisers to positions.

Example Two positions with 200, 100 clicks Three bidders with values $2, $1, $1 Efficient assignment is assortative Supporting (stable) prices

Bidder 2 pays $100 for slot 2, (or p2 = $1 /click).High enough to deter bidder 3 => at least $100, but

not so much that bidder 2 wants to drop out.

Bidder 1 pays $200-300 for slot 1, p1 [1,3/2].High enough to deter bidder 2 => at least $200, but

not so much that bidder 1 wants to drop down.

Example, continued Two positions with 200, 100 clicks Three bidders with values $2, $1, $1 GSP equilibrium

Efficient matching, payments of $1, and $p1. Bids required to support these payments

Bidder 3 bids $1 per click Bidder 2 bids $p1 [1,3/2]. Bidder 1 bids at least p1

Easy to check that no bidder benefits from deviating…

For each set of competitive prices, there is a set of GSP eqm bids, and vice-versa…. Revenue is $100 + $(200-300), or $300 to $400 total.

Compare to Vickrey auction

Two positions with 200, 100 clicks Three bidders with values $2, $1, $1

Vickrey auction Efficient matching. Bidder 2 pays $100 (displacing 3) Bidder 1 pays $200 (displacing 2,3) VCG payments are $100, $200. Total $300.

GSP prices are at least as high as Vickrey!

Another example Three positions with 300, 200, 100 clicks Four bidders with values $3, $2, $1, $1 Efficient assignment is assortative Supporting (stable) prices

Bidder 3 pays $100 for slot 3, p3 = 1.

Bidder 2 pays $200-300 for slot 2, p2 [1,3/2].

Bidder 1 pays $400-600 for slot 3, p3 [4/3,2].

Relationship between VCG and GSP eqm VCG payments are $100, $200, $400, revenue $700. GSP payments range from $700 up to $1000.

Stable prices, generally

Stable prices satisfy

(vk - pk) • xk (vk – pk-1) • xk-1

(vk - pk) • xk (vk – pk+1) • xk+1

Re-arranging we get

pk-1xk-1 pk xk + vk(xk-1-xk)

pk-1xk-1 pk xk + vk-1(xk-1-xk)

This gives us a relationship between price of one slot and the price of the slot above… can solve for stable prices from the bottom up…

Features of Equilibrium

Allocation is efficient (assortative)

Increasing price of marginal clicks Varian points out this is testable.

Implies bidders are click-constrained!

Pricing should be linear if bidders satiated…

Bids “reveal” bounds on bidder values. Apparently not so easy to invert in practice.

Actual bidding is surprisingly unstable…

Ascending auction What if there is incomplete information about

values – does this change things, or is there a naural process through which market equilibrates?

Suppose price rises from zero, advertisers can drop out at any time, fixing their bid.

Theorem (Edelman et al.). There is a unique perfect equilibrium in which advertisers

drop out in order of their values. The equilibrium is efficient and the prices are Vickrey. The equilibrium is an ex post equilibrium – no one wants to

go back and change their bidding after the auction ends.

Choices in Auction Design

How many slots to sell? Would search engine want to restrict slots available?

Could this ever increase revenue? Efficiency?

Setting a reserve price? What is the optimal reserve price?

Is it better to use a reserve price, or restrict slots?

Clickability and “squashing” What if ads have different “clickability”

Should you incorporate this in the auction? How?

Example: Slot Restriction Two positions with 200, 100 clicks Three bidders with values $2, $1, $1 Should the seller sell only one position?

Focus on lowest equilibrium (Vickrey) prices. Selling two positions: revenue of $300. Selling one position: revenue of $200.

Bidder 2 and 3 will pay up to $1 per click.Market clearing price is $1 per click for Bidder 1.

Example: Slot Restriction Two positions with 200, 100 clicks Three bidders with values $3, $3, $1 Should the seller sell only one position?

Selling two positions: revenue of $500.Bidder 2 will pay $1 /click for slot 2Bidder 1 will pay $2 /click for slot 1

Selling one position: revenue of $600.Bidder 2 will pay up to $3 per click for slot 1Market clearing price is $3 per click for Bidder 1.

Example: Reserve Prices Two positions with 200, 100 clicks Three bidders with values $2, $1, $1 Can the seller benefit from a reserve price?

No reserve price: revenue of $300. Reserve price of $2: revenue of $400

Sell only one position, but for $2 per click!

Example: Reserve Price Two positions with 200, 100 clicks Three bidders with values $3, $3, $1 Can the seller benefit from a reserve price?

No reserve price: revenue of $500 (or $600 if sell just one position).

Reserve price of $3 (and sell both positions): revenue of $900!

In general, is it better to use a reserve price, or to adjust the number of slots for sale?

Bidder-Specific Click Rates Some ads may be more relevant than others.

eg if query is “Pottery Barn,” what ad will get clicked?

Extended model where click rates differ. Suppose Pr(click) = aixk

Values: uik= vi (ai xk)= (vi ai )xk

Bids are still made on a per-click basis

Value rank: rank bids by expected revenue, by bi ai Eqm allocation will maximize total value. Bidder-optimal eqm will be payoff-equivalent to Vickrey

Bid rank: rank bids directly by bi . May not be efficient, but may raise revenue.

“Squashing” Example

Two positions with 200, 100 “base” clicks

Three bidders per-click values $2, $1, $1

click-thru rates: 2,1,1

Rank bids by bid*CTR Bidder 2 pays $1 per-click for position 2

Bidder 1 pays $0.50 per-click for position 1 (why?)

Total revenue: $1*100 + $0.50*400 = $300.

“Squashing” Example

Two positions with 200, 100 “base” clicks Three bidders

per-click values $2, $1, $1 click-thru rates: 2,1,1

Rank bids by bid (i.e. treat B1 “as if” CTR=1) Bidder 2 pays $1 per-click for position 2 Bidder 1 pays $1 per-click for position 1. (why?) Revenue: $1*100 + $1*400 = $500!

Can squashing would lead to inefficient matching of bidders and positions? When?

Issues not modeled Is each query a separate competition?

Advertisers really have portfolio of bids & broad match… They also have budget constraints, decreasing returns. They also have a choice between competing platforms.

Model doesn’t allow for much uncertainty Click rates, effectiveness of advertising are known. Seems to be a lot of experimentation in practice. Why?

Many aspects of search not captured How do people decide whether/what to click? Is there an interaction with “organic” search? “Broad match” and the use of algorithms… very important.

Platform competition

Current search market (approx.) Google: 70% market share, RPS maybe $0.08 Yahoo!: 20% market share, RPS maye $0.05 Microsoft: 10% market share, RPS maybe $0.04

Yahoo! and Msft strategic partnership Agreement from summer 2009, just approved. Searches on Y! will show Msft results and ads.

Questions: What explains the difference between the platforms,

particularly the difference in monetization? Are the platforms competing in a meaningful sense?

Platform competition, cont.

Scale economies: more searches means… Cheaper for advertisers to bid on a per-search basis, if

there are fixed costs to campaigns. Easier for advertisers to reach critical mass of consumers,

if they want to raise awareness. More possibilities for platforms to experiment, estimate

click rates and improve broad match algorithms.

How could we try to distinguish these hypotheses? Is scale a “barrier to entry” or “barrier to

competition”?

Platform competition Competition for users/searchers

Try to make algorithmic results “better” Syndication deals to “buy” searches

Competition for advertisers Is advertising on platform A a substitute for advertising on

platform B? Not immediately clear. If advertisers have diminishing returns or budget

constraints, yes – there is a “market for clicks”. How should will changes in the design of platform A

to impact the competition on platform B? Example: Yahoo! implements are reserve price system. Competition between auction platforms is analagous to

price competition but not as well understood.

Internet display advertising

Real estate on non-search web pages Wide variety of ads: text, graphical, video, etc. Wide variety of advertisers: “brand”, “performance,” etc.

Differences with search advertising Intent: search query makes it easier to discern users intent; Less

clear if user is reading their email or browsing the web. Search traffic is controlled by small set of firms that get to impose

standards, specify form of contract and design markets. Display advertising opportunities are controlled by many, many

publishers, so market is more fragmented. Result has been intermediaries (such as Google, but others as well) trying to create/design market for advertising to be traded.

Contract design Different types of contracts

Pay-per-impression (CPM): advertisers pay to have ad shown to a fixed number of “eyeballs”.

Pay-per-click (CPC): Advertisers pay for clicks. Pay-per-action (CPA): Advertisers pay for a “conversion” or sale,

or for some action (e.g. filling out a form post-click). Contract design involves trade-offs in

Incentives for publishers/advertisers Costs of certifying monitoring behavior and reporting Risk-sharing between advertisers and publishers.

Different advertisers/publishers use different contracts. Performance advertisers (CPC), brand advertisers (CPM) Large publishers (CPM), small blogs and publishers (CPC).

Market design Different models for advertising markets/sales

Large publishers typically have sales forces that negotiate sales of guaranteed impressions --- contracting can take place well in advance of delivery (e.g. buy now for August).

“Remnant inventory” is often sold through ad networks and exchanges. These are often spot auction sales. Advertisers submit bids, and market makers use algorithms to predict clicks and determine allocation.

Example: Google uses a version of its search auction to place search ads on non-query web pages (AdSense).

Market design questions: When should the market clear: Advance or real time? How should the market clear: posted prices or auctions? Will there be a “dominant” platform for ad sales?

Targeting and Conflation

Targeted advertising Traditional advertising involved limited targeting

(e.g. everyone watching Law & Order) Internet advertising allows advertisers to target

users based on demographics, geography, time, recent search behavior, etc.

Many believe that internet advertising will become progressively more targeted, with better and better “matching” of ads to users.

But, there are also costs to targeting!

Conflation

Evolution toward targeting means that each ad becomes its own “product”. This is not, historically, how markets have evolved.

Example: market for wheat (Debreu) Initially sold “by sample” each transaction different Standard contracts and grades of wheat allowed for thick

markets, futures contracts, lower transaction costs.

Conflation: treat things that aren’t exactly the same as the same in order to create better functioning markets.

Market Thickness

Targeting can create thin markets Facebook example, prices in spring 2009

Show ad to 1,000 Harvard undergraduates: $0.50 Show ad to 1,000 Havard econ majors: $0.05

What’s going on? This is a very thin market for ads shown to Harvard econ

majors, resulting in a low price! Targeting creates a large number of markets, some are

likely to be thin markets and this makes it hard to get all the prices right.

Conflation: treat econ majors as undergraduates, or at least apply undergraduate bids to econ major impressions.

Cherry-picking and “safety”

Targeting can also make markets “unsafe” by allowing savvy advertisers to cherry-pick

Example: Yahoo! Happy Contract McDonalds asks Yahoo! to show its ads only on sunny

days and when the stock market is up. This leaves Burger King and Wendy’s with the inventory on

rainy days when the market is down. Similar problems can arise in search auctions

Bid for auto insurance, but only in Palo Alto. Solutions: eliminate targeting? ensure advertisers a

“representative” set of impressions?

Conflation: search advertising

Search advertising appears very targeted: can bid for any of millions of keywords.

Yet there is also a lot of conflation One bid applies to all position on the page One bid (eg auto insurance) can be applied to many other

keywords (eg auto insurance companies). One bid applies to many users, and maybe to AdSense.

What is being “conflated” are clicks in different contexts. Conflation can mean same bid applies or is scaled mechanically according to an exchange ratge (e.g. a discount for AdSense clicks).

Targeting and Conflation

When many heterogeneous goods are being sold, there are important set of trade-offs in defining the products for sale…

Targeting, or finer product definition, means Improved (more efficient) matching, but Potential for thin markets Potential for cherry-picking

Conflation is a key element of market design

Simultaneous Ascending Auctions(and Radio Spectrum Licenses)

Today’s Lecture

Background on radio spectrum auctions The simultaneous ascending auction

Example, and “magic of the market” Theory of these auctions Evidence on how they work in practice What can go wrong, and why.

Next time: complex auctions, bidder strategy and innovative spectrum auction designs.

FCC Spectrum Auctions

Auctions to allocate radio spectrum Suggested by Coase (1960), and adopted by the FCC in

1994, followed by UK, Germany, Netherlands, Belgium, Mexico, India, etc.

Large auctions in which telecommunications companies may pay billions of dollars for spectrum licences.

Structure of typical auction Government (e.g. FCC) specifies a set of licenses to be

sold. Each license conveys the right to use a portion of the spectrum in a certain geographic area.

Licenses are sold in an auction, often using a simultaneous ascending auction designed by Milgrom-Wilson-McAfee.

Structure of the Problem

Potentially many different goods for sale E.g. license for San Francisco very different than

license for Death Valley. Potentially bidders with different objectives

E.g. Verizon may want spectrum to add 3G; rural telco might want spectrum for another purpose.

Substantial uncertainty about price/value Illiquid secondary market, not many licenses or

auctions, uncertainty about technology evolution.

Example

Two licenses: New York and San Francisco Three bidders: A, B, C.

NY SF

A 40 35

B 60 50

C 80 60

Let’s run an SMR auction… Efficient allocation: C wins #1, B wins #2.

SMR/SAA Rules

Simple case: each bidder allowed at most one license. Auction Rules

Seller sets initial price, and is the “high bidder” on each license. First round: each bidder can submit a bid for one of the licenses.

If a license gets multiple bids, a coin flip determines the new high bidder. If it gets no bids, the previous high bidder remains.

In subsequent rounds, bidders who are standing high bidders don’t bid, other bidders must submit a bit or else exit the auction.

Each new bid must be some increment (say 5% or 10%) above the standing high bid on a license.

The auction ends when there are no new bids. Each standing high bidder pays its current bid and receives its license.

SMR/SAA Rules

General case: bidders can bid for many licenses. Auction Rules

Seller sets initial price, and is the “high bidder” on each license. Bidders can submit bids on any set of licenses including raising

their own high bids, but must respect an “activity rule”. Bids must be at least an increment above the current price.

If a license gets one new bid, that bidder becomes the new high bidder. If no new bids, standing high bidder remains. If multiple new bids, a coin flip determines the new high bidder.

After each round of bidding, information about bids revealed. Auction ends when there are no new bids. Each standing high

bidder receives its license at its last bid price.

Why a simultaneous auction?

Relative to sequential auctions Bidders have more chance to coordinate their

bids on different licenses – may be important if bidders want to assemble packages.

Information is aggregated all at once – may be important if lots of uncertainty about value.

Should leads to greater degree of arbitrage and similar prices for similar items.

Why a multiple round auction? Relative to sealed bidding, information revelation…

Allows bidders to identify target licenses “on the fly” Mitigates inefficiency due to the winner’s curse Helps bidders to assess “roaming” opportunities.

The SAA design has some other virtues.. It’s transparent, and easy to check up on the gov’t. Activity rule prevents super-slow bidding.

Skeptics might argue… Design is vulnerable to demand reduction/collusion. Design does not facilitate new entry or “package” bidders.

Why an SMR auction?

Suppose we make the following assumptions: Each bidder places a dollar value on each of the licenses,

and wants to maximize its “profit” – equal to difference between value and price paid.

The government’s objective is efficiency, defined as allocating the licenses to maximize the sum of the dollar values of the winners.

The government does not know the license values of the bidders. (What if they did?).

We’re ignoring many potential complications, to which we’ll return.

The magic of the market

Bidding is “straightforward” if in each round bidders submit bids on the license that offers them the most profit at current prices.

Theorem. If bidders want one license (or multiple licenses but “substitutes” values”) and bid straightforwardly, the SMR auction leads to an efficient allocation and competitive eqm prices.

“Magic of the market” Auction outcome is “as if” the seller knew all the values and used

a computer to find the efficient allocation & mkt-clearing prices. Biders have “no regret” – at the final prices, each winner gets

exactly the license that gives it the most profit, and no loser would like to be a winner.

Put another way, the auction is a price discovery mechanism to find the efficient (market clearing) prices!

Example

Three bidders A, B, C. Two licenses: NY and SF.

NY SF

A 40 35

B 60 50

C 80 60

Efficient allocation: C wins NY, B wins SF. Let’s see how the SMR auction works (in theory)…

SMR Auction

Suppose prices start at $0, and the minimum raise is $1.

Initially everyone bids on NY. When prices reach $5, $0: A bids

on SF; B and C continue on NY. When prices reach $11,$1, bidder

B starts switching back and forth between NY and SF. (“arbitrage”)

When prices reach $45, $35, bidder A drops out, so B wins SF at $35 and C wins NY at $45.

NY SF

A 40 35

B 60 50

C 80 60

License Values

Alternative: “Vickrey” auction

Sellers asks bidders to write down their values and mail them in.

Seller allocates licenses to maximize total value.

Prices are set so that (two equivalent ways) Each bidder makes a profit equal to total value

with them in the auction minus the total value without them in the auction.

Each bidder pays the value he “displaces” by entering the auction and receiving his allocation.

Vickrey auction Efficient allocation gives $130

C gets 1, worth $80 B gets 2: worth $50

Without C, value would be $95 B would get 1, worth $60 A would get 2, worth $35 So C adds $130 - $90 = $35 in value. C values 1 at $80, so must pay $45.

Without B, value would be $115 C gets 1, A gets 2, so $80 + $35. So B adds $130 - $115 = $15. B values 2 at $50, so must pay $35.

Vickrey prices: $45, $35 - as in SMR!

#1 #2

A 40 35

B 60 50

C 80 60

License Values

Vickrey auction

Under the Vickrey rules, bidders do best to reveal their true values: it’s strategy-proof! If you bid more or less than your value, you don’t

change what you pay unless you change what you win.

If you bid more or less and it changes what you win, you make less profit.

Logic is similar to the other Vickrey cases we considered (T-bills & sponsored search).

Vickrey strategy Suppose B bids $60 and $0.

Then B wins 1, C wins 2.

Total value is $120 B’s value for 1 is $60 C’s value for 2 is $60

Without B, value would be $115 C gets 1, A gets 2, so $80 + $35. So B adds $130 - $115 = $15.

So B must pay $55 for #1 and makes a profit of only $5, less than the $15 it gets from truthful reporting.

#1 #2

A 40 35

B 60 50

C 80 60

License Values

SMR auctions in practice

SMR auctions (and “clock auction” variants) are very common for spectrum and other goods.

What is the evidence on their performance? We’ll start with a very successful UK auction,

Then we’ll look at some European auctions that weren’t so successful and think about what can go wrong.

Next time, we ‘ll discuss some of the US auctions, which are often more complicated, and sometimes surprising.

Finally, we’ll talk about some innovative new auction designs that are starting to be used, and their properties.

UK Auction of 3G Spectrum

In 1998, British Radiocommunications Authority (RA) was designated to sell spectrum licenses for third generation (3G) wireless services.

The RA decided to follow the FCC and use an auction: banks estimated an auction might raise £500 million ($750 million).

The RA employed a small group of auction designers. Paul Klemperer (former Stanford GSB student, and

my advisor at Oxford) was principal auction theorist. Economists Jeremy Bulow of Stanford GSB and Ken

Binmore of LSE were also involved.

Deciding what to Sell

An important question is what to sell How many licenses? Exactly what spectrum? In this case, european countries had agreed to all

designate certain spectrum for 3G use; the main question was whether to sell 4 or 5 licenses.

Licenses grant owner the right to use the spectrum, and an obligation to build out a network of cell towers to provide coverage. More service is desirable, but concern as to whether it was

reasonable to expect buildout of five separate networks.

Identifying Bidders

There were four incumbent phone companies in the UK, operating “2G” services. Vodafone, Orange, British Telecom, One-to-One.

Complication: Vodafone was trying to take over Mannesman, which owned Orange. Vodafone had agreed to divest Orange, but post-auction.

Gov’t decided to let both Vodafone and Orange bid.

Now, the big problem: what auction design to use, and would the design attract several other bidders?

Ensuring competition

SMR auction is efficient and prices are competitive given the set of bidders who participate

assuming bidding is straightforward

In the UK, entry was the serious concern With four licenses, and four strong incumbents, new

bidders might not bother to show up.

Without a new bidder, prices might be very low.

The bidding team considered an “Anglo-Dutch” design – SMR until five remaining bidders, then a final sealed bid round … could this have helped?

What happened

The RA finally decided to sell five licenses. License A reserved for a new entrant

Licenses A, B a bit bigger than C,D,E.

Bidders can only bid on one license at a time

In first round, everyone bids whatever they want on one of the five licenses – then single increment bids.

There were thirteen entrants in total Incumbents plus nine entrants including major players like

Telefonica, Hutchinson Whampoa, etc.

What happened

What happened

Auction ends after 150 rounds….

Success in the UK

Four incumbents and one entrant won licenses.

Auction netted £22 billion, about $39 billion dollars – “the biggest auction ever”.

Some other auctions held around the same time, however, were not as successful….

Entry problems

Netherlands auction of 3G spectrum in 1999.

Following UK lead, decided to sell five licenses using an SMR auction.

However, there were some differences The Netherlands has five incumbent (2G) operators.

There was no prohibition on bidding partnerships.

What happened?

Netherlands auction

Prior to auction, major outside telecom firms (Deutsche Telekom, DoKoMo, Hutchinson Whampoa) all reach partnership agreements with an incumbent.

This left just one entrant, a startup called Versatel.

What happened in the auction On day 1, Telfort (owned by BT) sends Versatel a letter saying

that it “can’t win” and should drop out immediately!

Versatel shortly drops out: total revenue of 3bn euros – at UK prices, auction would have raised 10bn euros.

Bidding problems

German GSM auction in 2000. Ten nationwide licenses. Bidders allowed to win multiple licenses. First bid at 10m DM, then 10% price increments. Bidders: two very strong bidders, Mannesman

and T-Mobile, and some small guys.

What might you be worried about here?

German GSM Auction

What happened in the auction Round 1: Mannesman bids 36.6m for each of 5

bands, and reduces eligibility. Round 2: T-Mobile (Deutsche Telekom) bids 40m

for the other five bands, reduces eligibilty. No bids in round 3!

Complications

Even in the UK setting where things look nice, one might be worried about a number of issues Consumers might care who are the winners: maybe “total

value” isn’t the right objective. Firms may care who are the other winners, or may be just

learning their values in the auction. The SMR is designed for efficiency, but maybe isn’t the

design that maximizes revenue. Maybe competitive prices are too high – because they

leave firms without enough money to build their networks. The SMR design didn’t deal with the problem of how many

licenses – the Germans tried to, but with limited success!

Conclusion

Magic of markets: auctions can be a powerful tool for price discovery and efficient allocation.

But plenty of things can go wrong. Successful auctions need to: Induce bidders to participate Induce bidders to bid competitively

Considerations around the auction must be accounted for (what to sell, what are the objectives, etc.): “The auction is always bigger than you think!”

Spectrum Auctions:Strategy and Design

Today’s Lecture

Simultaneous Ascending Auctions

Bidder strategy in “complex” auctions The exposure problem Budget constraints and forecasting The AWS auction

New auction designs

Refresher: SAA Rules

Auction consists of multiple rounds. Round begins with standing high bid on each license

(initially the seller), and a minimum bid increment.

Each bidder can submit bids on any number of items, subject to an eligibility and activity rule.

If no bids on a license, standing high bidder remains. If multiple bids, one bid selected at random to be high bid.

Information about bids is revealed to bidders.

Auction ends when no new bids are submitted.

Theory of SMR auctions

Suppose bidders view licenses as substitutes and bid straightforwardly, i.e. each round bid for most desired licenses at current prices. Then,

Arbitrage: the final prices for identical items will differ by at most one bid increment.

Competitive equilibrium: the final prices will approximately competitive equilibrium prices.

Efficiency: If the bid increments are small, the final license

allocation will be efficient.

Results due to Gul and Stacchetti (2000), Milgrom (2000).

SAA auctions in practice

SAA auctions (and “clock auction” variants) are very common for spectrum and other goods.

What is the evidence on their performance? In the UK spectrum auction, the SMR auction appeared to

work very well – simple setting, not much strategy.

In some other European auctions, we observed problems.

Now we’ll look at some evidence from US auctions, where things are often more complicated, and surprising.

Focus on elements that create role for strategy Exposure problem, activity rules, budgets & complexity.

The exposure problem

New entry may require a package of licenses

Danger for entrant: might end up with very expensive spectrum but not enough for viable entry.

Why not re-sell? Problems include opponent budgets, other package bidders, bargaining and agency problems.

Fear of being “exposed” to losses can lead to conservatism, and auction outcome may not be efficient.

Exposure problem is caused by uncertainty.

Bidders may have to make committing bids early in the auction, when they are uncertain about how much it will cost to complete their target package.

Exposure problem

Two licenses A and B Entrant has value 100 for the pair, else zero. Individual bidders for A, B with values U[0,125]. Suppose A is sold first, followed by B.

Solve for entrant’s optimal strategy In entrant loses A, won’t bid for B and gets profit = 0. If entrant wins A, will bid to 100 for B (why?) and expects a

profit (4/5)* [100 – 50] – pA = 40 - pA

Therefore in the first auction, entrant will bid up to 40.

Efficiency vs equilibrium

pA

pB

100

00 125

Entrantwins bothlicenses

Entrant winsA only

PROFIT

LOSS

125

Efficient for Entrant towin if individual bidder values are inside pink line,ie if 100 > pA + pB.

100

Strategy for exposure problem

Strategy can potentially resolve uncertainty.

Example Entrant has value 100 for the pair A & B.

Individual bidder for A has value U[0,100]

Individual bidder for B has value U[0,60]

Possible ways the auction could go A sells first, B sells first, or prices rise together?

Entrant may be able to have some control over this.

Auction timing

Suppose license B sells first If entrant wins B, expects to pay 50 for A.

Value of winning B: 100 – 50 – price of B

Optimal strategy: stop bidding at pB=50.

Expected profit 20.8.

Suppose license A sells first If entrant wins A expects to pay 30 for B.

Value of winning A: 100 – 30 – price of A.

Optimal to stop on A at pA=70, exp. profit 24.5.

Controlling the Pace

Best case for the entrant Prices rise on both licenses, but faster on A.

If and when prices reach pA=60, pB=20, entrant exits.

At pA=60, pB=20, value of winning A (or B) is zero. Expected profit is 25.3.

Idea: entrant should raise prices in a way that provides the most information before becoming committed to a purchase.

Strategic individual bidder

Entrant with value 20 for licenses A & B together.

Two individual bidders License A bidder with value 10

License B bidder with value cB ~ U[0,30]

License B bidder prefers to see price on A rise first. Entrant will exit when pA= 5, so possible to buy B for zero.

License B bidder can use strategy to exacerbate the exposure problem for the entrant!

Activity Rules

Activity rules necessary to keep auction moving Each license assigned some number of points Bidder start with eligibility points, must use them each

round or else have their eligibility reduced. Problem for a “package bidder” – creates exposure risk.

Activity rules also complicate arbitrage Suppose NY worth 200, LA worth 100, SF worth 100. If you’re high on NY and get bid off, can switch to SF/LA,

but what if you’re high on SF/LA and are bid off LA only? Serious issue if some licenses much bigger than others!

Activity rules and timing

Strategy to deal with activity rules Bidders can “park” points to save them for later. Bid on large licenses to maintain “flexibility”

Auction timing: this suggests that… Bidding will tend to start on large licenses; Large license licenses will tend to “clear” first. Similar licenses may not sell for the same price.

Bidding activity (FCC auction 35)

Fraction of bids on large licenses

Fraction of bids on small licenses

Timing of final bids (auction 35)

Round of final bid plotted against license size in bid units

Large licensesclear first

Variation inclearing round

The AWS Auction

Use FCC’s auction of Advanced wireless service in 2006 to illustrate bid strategy and features of large auctions.

This was a large, complicated auction with a very surprising outcome that has subsequently influenced auction design.

US sale of AWS spectrum (2006)

Background for the auction

90 MHz of nationwide spectrum, 1122 licenses Regional licenses (10,10,20 MHz), 6 to cover US Smaller licenses (10,20,20 MHz), 176 to cover Total of 168 bidders, including major incumbents, smaller firms. Two potential national entrants: SpectrumCo and WirelessDBS.

Entrants face a difficult problem Theory doesn’t provide much guidance on how to bid in a way

that avoids the exposure problem…

SpectrumCo problem

Goals for the auction Acquire 20 MHz of spectrum covering 85% of US

population, without spending more than budget. If this is impossible, don’t buy anything?

Strategic thinking Beware the exposure problem! Try to figure out how much it will cost to buy target

amount of spectrum… but how?

Hard to forecast prices!

Role of bidder budgets

Many bidders appear to be limited by budgets, rather than values --- a neglected but important pattern.

With many substitutable items for sale, a straightforward bidder will eventually bid its budget and continue doing so each round.

Even if some bidders don’t behave this way, aggregate demand elasticity will be anchored around -1 as prices rise.

Empirical proposition:

Auction “exposure,” defined as sum of all bids in a round should rise faster than auction revenue and level off at final revenue.

“Exposure” forecasts prices

Sum of high bids (revenue)

Sum of all bids (exposure)

FCC Auction 35

Forecasting in the AWS auction

Sum of high bids (revenue)

Sum of all bids (exposure)

FCC AWS Auction

Not everyone is a budget bidder

T-Mobile

Dolans

Exposure of individual bidders in the AWS auction

Spectrumco

Applying the budget hypothesis

Why is an accurate forecast of final prices useful? Avoid exposure problem: allows an entrant to identify if a desired

aggregation is achievable at reasonable price.

Acquire licenses cheaply: allows a bidder to anticipate price

anomalies if licenses clear in sequence.

Would budget forecasting have worked in past auctions?

Requires exposure to peak sufficiently early.

Requires exposure not to overshoot final revenue.

Exposure peaks early in auction

Peak/final exposure FCC sales

Overshooting in “small” auctions

No overshoot in large auctions

How the AWS auction worked

Recall basic structure of licenses: “Large” regional licenses (three bands, 40 MHz) “Small” EA/CMA licenses (three bands, 50 MHz)

Competitive landscape: 168 bidders, major incumbents, and two potential national entrants SpectrumCo: cable TV consortium Wireless DBS: satellite TV consortium

Controlling the pace

Bidding started on large regional licenses. But due to uniform starting point, prices rose uniformly on

coasts/interior, creating serious exposure problem…

In round 9, Spectrumco makes maximum possible jump bid on all Northeast and West regional licenses, doubling their prices from $750m to $1.5 billion.

Shake-out: Wireless DBS takes waivers, then exits. FCC eliminates jump bidding in subsequent auctions. But prices continue to rise on the REAG licenses…

Rising prices in AWS auction

Budget forecasting

At round 13, the situation is High bids on REAGs (40 MHz): $5.0 bn High bids on EA/CMAs (50 MHz): $0.7 bn Auction exposure had peaked at $14.2 bn.

Cable consortium gives up REAG licenses and switches to smaller licenses, other major bidders do not.

Why did no other large bidder switch? Large licenses “easiest” way to buy large quantity and no

reason a priori to expect they’d be much more expensive. Incumbents did not face exposure problem: less need to

forecast prices and “discover” budget theory.


Spectrumcoband switch


Timing of final bids in AWS

Large REAG licenses

Another exposure problem

At round 19, the situation is High bids on REAG licenses: $7.6 bn High bids on EA/CMA licenses: $2.3 bn

Budget algebra Implied maximum budget for small licenses: $6.6 bn. Estimated price of 20 MHz national: $2.6 bn.



Price per MHz-pop of REAG licenses

Price per MHz-pop of EA/CMA licenses







Similar spectrum, different prices

US auction of AWS spectrum (2006)

Band MHzLicense

type Price

($/MHz-pop)Price (US 10Mhz)

A 20 CMA $0.40 $1.1 bn

B 20 EA $0.43 $1.2 bn

C 10 EA $0.52 $1.5 bn

D 10 REAG $0.62 $1.8 bn

E 10 REAG $0.61 $1.7 bn

F 20 REAG $0.73 $2.1 bn

SpectrumCo’s Licenses (20 MHz)

Failure of price arbitrage

Table 1: Prices Paid by the Five Largest Buyers in the AWS Auction

Bidder Total Amount Paid MHz-Pops Price per MHz-Pop

SpectrumCo $ 2,377,609,000 5,267,189,470 $ 0.45

Cingular 1,334,610,000 2,436,458,880 0.55

T-Mobile 4,182,312,000 6,638,718,070 0.63

Verizon 2,808,599,000 3,840,952,220 0.73

MetroPCS 1,391,410,000 3,840,952,220 0.96

Four incumbents $ 9,716,931,000 14,361,573,190 $ 0.68

New auction designs

AWS auction spurred new designs 700 MHz auction in United States British WiMax auction

These auctions allow for “package bidding” British design also involves new twists

“Vickrey” or “near-Vickrey” payment rule Conflation in license definitions

US 700 MHz Auction

Three main bands A and B bands were 10MHz C band was 20 MHz, with special rules

Bidders allowed to submit a “package bid” for the entire national C band. Lobbied for by Google, although they didn’t buy. Package bidding favors entrants – can create a “threshold

problem” for smaller bidders!

In the auction, C band went at a huge discount.

British wimax auction

Very innovative new design to sell spectrum in the UK.

120 MHz of spectrum divided into 42 5-MHz blocks.

First stage clock auction

Seller calls out prices

Bidders call out number of blocks they want

Stage ends when Demand <= Supply.

Sealed bids: if overshoot in first stage, bidders can “add” bids.

Then, seller takes all bids and computes efficient allocation.

Bidders pay Vickrey prices, … but if Vickrey prices are too low (outside the core), prices are increased until the resulting allocation is in the core!

British WiMax, cont.

Auction also includes third stage Winners are guaranteed set amount of spectrum Third stage determines who gets which blocks. Sealed bid package Vickrey auction (with prices adjusted

up if result is outside the core).

Conflation in auction design Different items are treated as identical (conflated) Additional round used to “de-conflate” the items. Conflation is very common in setting up markets.

Conclusions

Simultaneous multi-round auctions are commonly used for selling radio spectrum, and many other goods.

Design has many advantages in terms of revealing information, giving bidders flexibility, but auctions can also be complex creating a role for strategy.

Innovative new designs such a British auction are trying to simplify the bidder problem…

Experience of Spectrumco shows how economic theory can be practical as well as fun!

Package Auctions

London Bus Routes

City of London auctions off service contracts for bus routes in Greater London.

How it works City decides bus network, frequency of buses, types of

buses, exact routing etc. – provision is outsourced.

City uses sealed bid auctions allowing bids for packages of routes as well as individual routes.

Bids state a fee to be paid to the city to operate the buses for five years – collected fares go to the city.

Why package bids?

Operator cost structure To operate routes, must have storage and maintenance

facility – fixed cost, can accommodate several buses.

So costs per route may decline if operator has several routes – at least until capacity is reached.

Bidding advantage in the auction Consider operator with zero cost on routes A,B.

Suppose opponent bids on A,B are U[0,10]

Bidding 5 for A, 5 for B => expected profit 2*5*(1/2)=5

Bidding 7.5 for A/B package => exp. profit 7.5*(3/4)=5.6!

London auction data

Source: Cantillon and Pesendorfer, “Auctioning London Bus Routes,” 2006

Package bid “discounts”

Note: marginal discount assigns full discount to smallest route in the package.

Interpreting the data

Cantillon-Pesendorfer try to infer if package bidding reflects cost synergies or is used strategically.

They estimate operator costs in the London market using the bid data…

Findings: Mininmal or no cost synergies!

Strategically use of package bids: bids are marked up over cost by 16.4% for individual routes, but only 11.4% for packages!

Package auctions

Package bidding allows bidders to express complex demands in multi-good settings. A set of bus routes in London

A set of spectrum licenses.

A set of airport take-off and landing slots

A complete search/display advertising campaign

Today: discuss underlying theory, different auction methods, and some evidence.

The problems begin… Two items for sale, A and B Two bidders with values:

A B AB

1 0 0 12

2 10 10 10

No item prices clear the market. Such prices must result in bidder 1 efficiently

buying both: pA10, pB10, and pA+pB12!

SMR auction

Suppose everyone know values (complete information) Bidder 1 should not bid!

Bidder 2 will win one item at a very low price.

With uncertainty about opponent values Bidder 1 may start bidding but will have to pay 10 for each to win both.

More likely outcome – bidders split items, perhaps at low prices.

The outcome is likely to be inefficient and maybe yield low revenue. Although recall Spectrumco overcoming exposure problem.

A B AB

1 0 0 12

2 10 10 10

Package bids in the SMR

Allow bidders to make “package bids” - e.g. $X for the package of items A and B.

SMR with package bidding Each round, there is a provisional winner for each license –

some provisional winning bids could be package bids.

Bidders can submit new bids, individual or package, for any licenses they like.

Seller takes new bids and existing bids (maybe including losing bids) and identifies highest revenue allocation.

Auction ends when no new bids are submitted.

Auction of 700 MHz spectrum

US auction of 700 MHz spectrum in 2008. B block: 10 MHz divided into 176 EA licenses C block: 20 MHz divided into 6 REAG licenses Bidders can make a national bid on the C block.

What happened? Little bidding on C block – Google bid the reserve price,

and Verizon bid a bit higher. Lots of bidding on the B block – prices about 4x that of the

C block. But many other special features of the auction make it hard

to identify the exact effect of package bidding.

Threshold problem

SMR with package bidding Suppose bidder 1 starts by bidding 10 for AB. Bidders 2 and 3 have to make bids that sum to 11. Incentive to wait for other bidder to increase its bid. But then auction could end with inefficient package winner!

A B AB

1 0 0 12

2 10 0 10

3 0 10 10

Who gets the advantage?

It is hard to balance the playing field when some bidders have package preferences Individual bidding: creates difficult exposure

problem for complements bidder. Package bidding: creates difficult threshold

problem for individual bidders.

Why package bidding changes things Effectively gives package bidder a chance to

move second – e.g. bid 10, and let the auctioneer divide up the bid once the other bids are in!

Vickrey auction

Vickrey auction with package bidding Bidders submit their values for all possible

packages (could be a lot -- 2N) Seller finds highest value allocation, sets prices

so that each bidder makes as profit the difference between value with them and without them.

Desirable properties The outcome is efficient if bidders are truthful. Truthtelling is a dominant strategy

Vickrey auction: problems Consider our “threshold problem” example

A B AB

1 0 0 12

2 10 0 10

3 0 10 10

Bidders 2 and 3 win items. Each pays a Vickrey price of 2 => revenue 4. BUT, package bidder would pay 10!

Vickrey auction: problems Now suppose bidder 2,3 have lower values

A B AB

1 0 0 12

2 3 0 3

3 0 3 3

With honest bidding, package bidder wins. If bidders 2,3 report 10, each wins and pays 2 Small amount of collusion has a big effect!

Vickrey auction: problems Bidders may also want to split their bidding

A B AB

1 0 0 12

2 0 0 11

Honest bidding means 1 wins and pays 11. Bidder 2 can enter as 2A, 2B, each bidding 10

for a single item – wins both and pays 4! If bidders 2A, 2B bid 11 each, they each win and

pay 2, so higher bids can mean lower revenue!

Budget constraints

We saw that budget constraints seem to be important in spectrum auctions.

They pose a big problem for Vickrey auctions Suppose items A, B are for sale.

Bidder values A at 200, B at 100, budget of 150.

Can’t bid true values and be sure to stay under budget.

“Straightforward” bid of 150 for A, 100 for B and 150 for the pair implies zero value for B if awarded A.

Bidding with a budget & vickrey rules is complicated!

Core outcomes In markets with complements, market

clearing prices may not exist.

“Core” allocations are a useful generalization. An allocation is in the core if there is no set or

“coalition” of players that could make a deal on their own from which all of them would benefit.

“All gains from trade are exploited”

The “bad” Vickrey examples are cases where the Vickrey outcome is not in the core.

Vickrey and Core outcomes Same example as before

A B AB

1 0 0 12

2 10 0 10

3 0 10 10

Bidders 2 and 3 win items, pay 2 each. But package bidder would pay 10! That is: the auction outcome is not in the core!

Core outcomes and auctions

There is always at least one core allocation Example: assign items efficiently, have buyers

pay their full value to the seller. Problem: unclear how to get bidders to reveal

values! Day and Milgrom (2008) propose to use

“core-selecting” auctions in which: Bidders are asked to submit bids Bids are treated as values. Seller finds core allocation that is bidder optimal.

Auctions vs exchanges

With one seller, there is a core allocation. Bidder 1 wins the object, pays between 10 and 12.

But if goods A and B belong to different sellers, the core is empty, because… Bidder 2 must get 0 Coalition of either seller and bidder 2 must get 10 So, each seller must get 10, but only 12 is available.

A B AB

1 0 0 12

2 10 10 10

Pay as bid auctions

London bus routes are a “pay-as-bid” auction Bidders submit bids Bids treated as values to find efficient allocation Bidders are asked to pay bids (seller optimal).

Bernheim and Whinston (1986, QJE): the full information Nash equilibria of the pay-as-bid package auction correspond to the set of bidder-optimal core allocations.

Pay as Bid Auction

A B AB

1 0 0 12

2 10 10 10

Bidder 1 bids 10 for package A/B Bidder 2 bids bA and bB that sum to 10. Allocation is efficient, revenue is 10.

Pay as bid Auction

Bidder 1 bids 12 for the package Bidders 2, 3 submit bids that

Are each less than 10, and sum to 12. Allocation is efficient, revenue is 12.

A B AB

1 0 0 12

2 10 0 10

3 0 10 10

Experimental evidence

Does package bidding really help? Published reports of experiment suggest remarkable

efficiency properties.

Porter et al (2003, PNAS): efficiency of 100% in 23 of 25 trials, 99% in the other two!

Hard to interpret these results As number of items grows, the number of possible values

to use in the experiment grows as 2n - huge!!

Are these experiments focused on “easy” cases?

Easy and hard settings

Straightforward bidding in SMR auction: in each round, bid for most desirable set of items at current prices.

Kagel-Lien-Milgrom (2009) Setting is “easy” if straightforward bidding in SMR

with package bidding leads to efficient outcomes, otherwise is “hard”.

Use computer simulations to classify different settings as easy or hard, then run human experiments to see if difficulty of the setting matters.

KLM experiment design

KLM Results

KLM results, cont.

Summary of theory

If the bidders view goods as substitutes, then Competitive equilibrium (CE) prices exist. There is a CE with “minimal prices”. This CE coincides with Vickrey auction outcome. This CE is a core allocation.

In the general package preference case CE prices may not exist Vickrey auction may not yield core allocation. Non-Vickrey designs do not encourage truthful bidding Auctions suffer from exposure/threshold problems.

British wimax auction Very innovative new design to sell spectrum in the UK.

120 MHz of spectrum divided into 42 5-MHz blocks.

First stage clock auction

Seller calls out prices

Bidders call out number of blocks they want

Stage ends when Demand <= Supply.

Sealed bids: if overshoot in first stage, bidders can “add” bids.

Then, seller takes all bids and computes efficient allocation.

Bidders pay Vickrey prices, … but if Vickrey prices are too low (outside the core), prices are increased until the resulting allocation is in the core!

British WiMax, cont.

Auction also includes third stage Winners are guaranteed set amount of spectrum Third stage determines who gets which blocks. Sealed bid package Vickrey auction (with prices adjusted

up if result is outside the core).

Conflation in auction design Different items are treated as identical (conflated) Additional round used to “de-conflate” the items. Conflation is very common in setting up markets.

Conclusion

Package auctions are finding increasing use for hard resource allocation problems.

Vickrey auctions problematic because of low revenue, non-core outcomes.

Alternative designs (pay-as-bid, Vickrey, SMR, etc.) trade off incentive and distributional properties.

Package exchanges are fundamentally hard due to empty cores, but some interesting new ideas are being studied here as well.

Documents

Auction Markets Jon Levin Winter 2010 Economics 136