Statistical mechanics of combinatorial auctions

TL;DR

This paper models combinatorial auctions using statistical physics, revealing phase transitions between easy and hard computational regimes, and introduces an iterative algorithm for solving large instances.

Contribution

It applies statistical mechanics to analyze auction complexity, identifies phase transitions, and develops an iterative algorithm for large-scale auction problems.

Findings

Identifies easy and hard computational regimes in auctions.

Develops an iterative algorithm for large instances.

Discusses competing states of revenue and bidder satisfaction.

Abstract

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.