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AKSOE: Arbeitskreis Physik sozio-ökonomischer Systeme

AKSOE 7: Economic Models and Evolutionary Game Theory I

AKSOE 7.1: Talk

Tuesday, March 27, 2007, 10:15–10:45, H8

Combinatorial auctions as frustrated lattice gases — •Tobias Galla^1,2, Michele Leone³, Matteo Marsili¹, Mauro Sellitto¹, Martin Weigt³, and Riccardo Zecchina¹ — ¹International Centre for Theoretical Physics, Strada Costiera 11, I-34014 Trieste, Italy — ²SISSA-CNR-INFM, Via Beirut 2-4, I-34014 Trieste, Italy — ³ISI Foundation, Viale S. Severo 65, I-10133 Torino, Italy

Combinatorial auctions are auctions in which bidders bid on combinations of items, as opposed to single items in conventional formats. The winner-determination problem of such multi-item auctions turns out to be non-trivial and computationally complex due to overlapping bids and overall frustration. In particular, the highest bid is not guaranteed to win.

We show how combinatorial auctions can be formulated as frustrated lattice gases on sparse random graphs, allowing the determination of the optimal revenue by methods of statistical physics. Transitions between computationally easy and hard regimes are found and interpreted in terms of the geometric structure of the space of solutions. We introduce an iterative algorithm to solve intermediate and large instances, and discuss competing states of optimal revenue and maximal number of satisfied bidders. The algorithm can be generalized to the hard phase and to more sophisticated auction protocols.