Internet Economics Class 4 Multiunit auctions 1 Multiple

Internet Economics כלכלת האינטרנט Class 4 – Multi-unit auctions. 1

Multiple items • Goal: design auctions that allow for multiple kinds of items – Items are non identical. • Examples: – Spectrum licenses covering different areas. – Baskets of financial assets. – Transportation of packages. – Advertising campaigns – Industrial equipment.

Desired properties • What would be desirable properties of such auctions? – Auction finds “market clearing” prices. – In equilibrium. . . – Auction rules are simple. – Robust to collusion, false-name bids, timing manipulations, etc. – Tractable: ends in reasonable time, bidders can compute their equilibrium strategies. • Bidders should not be expected to process or to report large amounts of data.

Challenges • Sealed-bid auctions? – Problematic. Bidder preferences may be complex. • Market-clearing prices may not exist – Especially when items are complements. • Bidders do not always know their preference… – Determining the preferences is often costly. • Do bidders know the equilibrium strategy in the complex auction?

Combinatorial preferences • Why shouldn’t we auction each item separately? • Auctioning each item alone ignores: – complements: v(TV) + v(VCR) < v(TV+VCR) – Substitutes: v(TV Toshiba) + v(TV Sony) > v(both TVs) • Bidding for packages (or bundles) may increase the efficiency of the auction.

Combinatorial preferences • We will next demonstrate the main ideas via a simple model: unit-demand bidders – Each bidder wants at most one item (but items are still nonidentical) • Non identical items: a, b, c, d, e, • Each bidder has a value for each item vi(a), vi(b), bi(c), . . • Each bidder wants one item only.

Example a b c Bidder 1 10 7 4 Bidder 2 0 8 5 Bidder 3 5 5 1 • What is the VCG outcome? 1. What is the efficient allocation? 2. VCG payment for Bidder 1? – Without Bidder 1, others gain 13. – With him, they gain 10. àp 1=3 Similarly, p 2=0, p 3=3. 7

Assumptions • Seller’s goal: maximize efficiency – By law for FCC spectrum auctions. • Seller does not know the values of the bidders – Here, even no distributional assumptions. • “Activity rule” – bidders must send bids constantly, otherwise be removed from the auction. – Prevents slow bidding and “sniping”.

Simultaneous Ascending Auction 1. Start with zero prices. 2. Each bidder reports her favorite item q Provisional winners are announced. 3. Price of over-demanded items is raised by $1. q Following bids by losing bidders. 4. Stop when there are no over-demanded items. – Provisional winners become winners. Claim: this auction terminates with: (1) Efficient allocation. (2) VCG prices ( ± $1 ) 9

Example a b c Bidder 1 10 7 4 Bidder 2 0 8 5 Bidder 3 5 5 1 • Let’s run the ascending-price auction now… • VCG payments: Bidder 1 pays 3 for a Bidder 1 pays 0 for c Bidder 3 pays 3 for b 10

Spectrum Auctions • The ascending auction we saw is called: Simultaneous Ascending Auction – Also known in the literature as tatonnement • Was introduced in 1994 for spectrum auctions. – Revolutionized the sale of spectrum. • Has been used since all over the world. • The basis of auctions for complex resource allocation problems. – Eg, transportation. 11

Why ascending price auction? • Simple and intuitive for bidders • “price discovery” – direct the attention of the bidders to the relevant items. – No need to determine the value of the other items/bundles. – For example: if they see an aggressive competition on one item, which become expensive, they may let it go. – Easier to assemble “packages” of items. • Decreases the amount of information broadcasted. – Again, bidders bid only on items that turn out to be relevant.

Equilibrium in the simultaneous ascending auction • Since the auction terminates with the VCG outcome, the auction is truthful. – Any deviation that leads to a different outcome will only hurt the bidders (same arguments as before). • This is more intuitive way to get to the VCG outcome – Analogous to 2 nd-price vs. Vickrey.

Market clearing prices • Conclusion: In a multi-unit auction with unit-demand bidders: This auction finds “market-clearing prices”: – every bidder receives his favorite item (given the prices) – all items are allocated (unless their price is 0). • The simultaneous ascending auction can be viewed as an intuitive way to reveal market-clearing prices. • The allocation that supports market clearing price is always efficient. 14

Why does it work? • For bidders that are interested in one item: the goods are substitutes. – If a bidder wants an Apple, and we increase the price of a Banana, the bidder will still demand an Apple. • This procedure actually reaches the efficient outcome for more general preferences. – As long the items are “substitutes”. • Example for complementarities: – Spectrum: covering contiguous areas. – Acquisition of two firms at the same business 15

Complementarities • This auction is problematic in the presence of complementarities. • Among the reasons: – Market clearing price do not exist. – Exposure problems. • What should one do with complementarities? – A problem. Not well understood. – Auction uses bundle prices. Or combinations of item and bundle prices. – More complex….

The exposure problem • bidders may have to make committing bids early in the auction, when they are uncertain about the eventual cost of the complete package. • Think about a new entrant to the spectrum market – Needs a certain minimal mass of spectrum to begin. – might end up with few very expensive spectrum, but not enough licenses. – Resell is not always possible • (opponents might have exhausted their budgets, legal problem etc. ) – Bidders fear of being “exposed” to losses, and this lead to conservative bidding and inefficiencies.

Next week • Online advertising • How search engines sell ads? • How users behave in search engines, and how it affects the ad market? 18