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Statistical mechanics of combinatorial auctions

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arxiv cond-mat/0605623 v2 pith:HZZGUYEN submitted 2006-05-25 cond-mat.stat-mech q-fin.ST

Tobias Galla , Michele Leone , Matteo Marsili , Mauro Sellitto , Martin Weigt , Riccardo Zecchina This is my paper · ORCID
classification cond-mat.stat-mechq-fin.ST
keywords algorithmauctionscombinatorialhardoptimalrevenuestatisticalallowing
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Combinatorial auctions are 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.

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