Auctions for Digital GoodsAli Echihabi

University of Waterloo – Nov 2004

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Talk Overview Review of four papers. New context, new approach. Focus on: “Competitive Auctions”, Goldberg,

Hartline, Karlin,Wright, Saks.

Extra: experiments and extensions. Discussion.

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Our Context Unlimited supply. Identical goods (digital). Utilities may vary a lot. Allocation no longer a problem. Pricing is. Holds for bounded supply. Why auctions then?

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New Approach What CS people do best! Algorithms are like auctions:

Correctness : Truthfulness Efficiency: Time Performance: Revenue

New concepts for auctions: Provable performance guarantees. Over all possible inputs.

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Competitive Auctions Bayesian can go wrong. Run detail-free auctions. Quantify the value of information:

How much revenue did we miss? What metric do we use?

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Benchmark Two metrics:

Maximum possible ever. You sell at bidder’s valuation. Multi-price.

Optimal price-fixing. Single-price for all bidders. We use this one.

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Definitions

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Definitions (2)

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Bid-independent Auction

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Important Result Deterministic Auctions are not competitive.

Symmetric: outcome is independent of the order of the bids.

Need to consider Randomized.

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Randomized Auctions Lower Bound:

Random Sampling:1. Dual-Price Sampling Optimal Threshold (DOST)

2. Sampling Cost Sharing (SCS).

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Definition of DOST

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Properties of DOST Truthful. More is better:

Best DOST can do is 4-competitive.

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Definition of SCS Special case of Moulin-Shenker mechanism A.k.a Consensus Revenue Estimate (CORE)

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Properties of SCS Truthful. 4-competitive. May lose half of potential profit:

Pick a ratio r < 1. Competitive ratio grows: 4/r.

Only sells if revenue reachable.

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Important Result: is good Competitive auctions do not outperform:

Considering all possible inputs.

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Results Summary No truthful deterministic auction is

competitive. Several randomized auctions are truthful and

competitive. is a good benchmark.

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Experiments: Number of Bids

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Experiments: Sample Size

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Experiments: Sample Size (2)

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Extensions: Online vs Offline Paper borrows concepts from online

algorithms That doesn’t make the auction online:

Decide the price of current bid before next bid arrives [3]

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Extensions: Envy Bidder X rejected. Bidder Y wins and pays a price

lower than X’s bid. Envy is bad for seller. No constant-competitive truthful auction is envy-

free. Relax constraints.

CORE: Consensus Revenue Estimate (or SCS) Truthful, envy-free, competitive, group-strategy proof

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Extensions: Online vs. Offline Using theory for online algorithms doesn’t

make your auction online. Online auction: determine price for bid i,

before next bid arrives. Can’t make all pricing decisions at once [3] gives a randomized online competitive

auction within

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Excellent References [1]: “Competitive Auctions”, Goldberg, Hartline,

Karlin, Wright, Saks.

[2]: “Competitive Auctions and Digital Goods”, Goldberg, Hartline, Wrigth.

[3]: “Incentive-Compatible Online Auctions for Digital Goods”, Bar-Yossef, Hildrum, Wu.

[4]: “Envy-Free Auctions for Digital Goods”, Goldberg, Hartline.

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Thank you!

Discussion