Single Parameter Combinatorial Auctions Lei Wang Georgia Institute of Technology Joint work with Gagan Goel Chinmay Karande Google Georgia Tech

Overview of Combinatorial Auction Setting  Mechanism  Allocation:  Payment:  Truthfulness  Social welfare

Our Model and motivation Motivation

Example: TV ad Auction

Our Model  Public function  Private value:  Valuations

Myerson’s Characterization of truthful mechanism  Monotone allocation:  Payment is determined Example: VCG mechanism Approximation algorithm might not be monotone

Our result:

Our conversion Plan:  Choose a range R  Run MIR  Show:

Construction of our range

Range

Properties 

Proof

Conclusion Conversion

Future direction Randomized mechanism  Randomized maximum in range  Randomized rounding

Truthfulness v.s. Approximability  Huge clash in non-Bayesian setting On the hardness of being truthful C.Papadimitriou and Y.Singer FOCS’08  No clash in Bayesian setting Bayesian algorithmic mechanism design J.Hartline and B.Lucier STOC’10 Towards Optimal Bayesian Algorithmic Mechanism Design X.Bei and Z. Huang SODA’11  Is there any clash for single-parameter?

Thank you! 谢谢