TY - GEN

T1 - Efficiency-Revenue Trade-Offs in Auctions

AU - Diakonikolas, Ilias

AU - Papadimitriou, Christos

AU - Pierrakos, George

AU - Singer, Yaron

PY - 2012

Y1 - 2012

N2 - When agents with independent priors bid for a single item, Myerson’s optimal auction maximizes expected revenue, whereas Vickrey’s second-price auction optimizes social welfare. We address the natural question of trade-offs between the two criteria, that is, auctions that optimize, say, revenue under the constraint that the welfare is above a given level. If one allows for randomized mechanisms, it is easy to see that there are polynomial-time mechanisms that achieve any point in the trade-off (the Pareto curve) between revenue and welfare. We investigate whether one can achieve the same guarantees using deterministic mechanisms. We provide a negative answer to this question by showing that this is a (weakly) NP-hard problem. On the positive side, we provide polynomial-time deterministic mechanisms that approximate with arbitrary precision any point of the trade-off between these two fundamental objectives for the case of two bidders, even when the valuations are correlated arbitrarily. The major problem left open by our work is whether there is such an algorithm for three or more bidders with independent valuation distributions.

AB - When agents with independent priors bid for a single item, Myerson’s optimal auction maximizes expected revenue, whereas Vickrey’s second-price auction optimizes social welfare. We address the natural question of trade-offs between the two criteria, that is, auctions that optimize, say, revenue under the constraint that the welfare is above a given level. If one allows for randomized mechanisms, it is easy to see that there are polynomial-time mechanisms that achieve any point in the trade-off (the Pareto curve) between revenue and welfare. We investigate whether one can achieve the same guarantees using deterministic mechanisms. We provide a negative answer to this question by showing that this is a (weakly) NP-hard problem. On the positive side, we provide polynomial-time deterministic mechanisms that approximate with arbitrary precision any point of the trade-off between these two fundamental objectives for the case of two bidders, even when the valuations are correlated arbitrarily. The major problem left open by our work is whether there is such an algorithm for three or more bidders with independent valuation distributions.

U2 - 10.1007/978-3-642-31585-5_44

DO - 10.1007/978-3-642-31585-5_44

M3 - Conference contribution

SN - 978-3-642-31584-8

VL - 7392

T3 - Lecture Notes in Computer Science

SP - 488

EP - 499

BT - Automata, Languages, and Programming

A2 - Czumaj, Artur

A2 - Mehlhorn, Kurt

A2 - Pitts, Andrew

A2 - Wattenhofer, Roger

PB - Springer Berlin Heidelberg

ER -