Approximations and Truthfulness: The Case of Multi-Unit Auctions

Auctions

Clean Air Auction

Definition of Multi-Unit Auctions

Can we obtain an algorithm that is fast, truthful and approximates the welfare

well?

Related Work

Theorem: There exists a truthful poly time randomized (1-)-approximation mechanism.

Theorem: There exists a poly time deterministic truthful ½-approximation mechanism.

Maximal in Range: limit the range and fully optimize over the restricted range.

The mechanism: (1)Split the items into n2 equi-sized bundles each of size m/n2.(2)Allocate these bundles optimally.

Theorem: Every maximal-in-range (½+)-approx algorithm requires at least m queries to the black boxes.

Proving Impossibilities:Characterize and Optimize

+ =

What’s Next?

Theorem: there exists a (1-)-approximation mechanism that is truthful in expectation.

The AlgorithmSome valuation function

Items

Value

Correctness

Summary

Open Questions

Basic Requirements from Auctions

This talk: auction design via multi-unit auctions.

Modern Auctions I: eBay

Modern Auctions II: Sponsored Search