Non-decreasing Payment Rules for Combinatorial Auctions

TL;DR

This paper introduces non-decreasing payment rules for combinatorial auctions, which prevent payments from decreasing with higher bids, enabling more efficient equilibrium computation and addressing issues with existing rules like VCG-nearest.

Contribution

The paper proposes non-decreasing payment rules, analyzes their properties, and develops a new algorithm that significantly improves the efficiency of finding approximate Bayes-Nash equilibria.

Findings

Non-decreasing payment rules prevent payment decreases with higher bids.

Many alternative payment rules are non-decreasing, unlike VCG-nearest.

The utility planes BNE algorithm outperforms existing methods by orders of magnitude.

Abstract

Combinatorial auctions are used to allocate resources in domains where bidders have complex preferences over bundles of goods. However, the behavior of bidders under different payment rules is not well understood, and there has been limited success in finding Bayes-Nash equilibria of such auctions due to the computational difficulties involved. In this paper, we introduce non-decreasing payment rules. Under such a rule, the payment of a bidder cannot decrease when he increases his bid, which is a natural and desirable property. VCG-nearest, the payment rule most commonly used in practice, violates this property and can thus be manipulated in surprising ways. In contrast, we show that many other payment rules are non-decreasing. We also show that a non-decreasing payment rule imposes a structure on the auction game that enables us to search for an approximate Bayes-Nash equilibrium much more efficiently than in the general case. Finally, we introduce the utility planes BNE algorithm, which exploits this structure and outperforms a state-of-the-art algorithm by multiple orders of magnitude.