iMLCA: Machine Learning-powered Iterative Combinatorial Auctions with Interval Bidding

TL;DR

iMLCA tackles the costly value-reporting burden in large combinatorial auctions by allowing bidders to submit upper and lower bounds on bundle values (interval bidding). It builds on MLCA by adding a bound-refinement process via a price-based activity rule and a Convergence Phase to guarantee a final allocation that can be determined from reports. The mechanism achieves the same allocative efficiency as MLCA while substantially reducing elicitation effort, and it outperforms the combinatorial clock auction in realistic spectrum-domain instances. Theoretical properties include individual rationality, no-deficit, and near-truthful incentives under practical assumptions, with empirical evidence based on SATS showing limited manipulation opportunities and favorable efficiency-cost trade-offs. Overall, iMLCA offers a practical, scalable approach for large ICAs where exact value elicitation is prohibitive.

Abstract

Preference elicitation is a major challenge in large combinatorial auctions because the bundle space grows exponentially in the number of items. Recent work has used machine learning (ML) algorithms to identify a small set of bundles to query from each bidder. However, a shortcoming of this prior work is that bidders must submit exact values for the queried bundles, which can be quite costly. To address this, we propose iMLCA, a new ML-powered iterative combinatorial auction with interval bidding (i.e., where bidders submit upper and lower bounds instead of exact values). To steer the auction towards an efficient allocation, we introduce a price-based activity rule, asking bidders to tighten bounds on relevant bundles only. In our experiments, iMLCA achieves the same allocative efficiency as the prior ML-based auction that uses exact bidding. Moreover, it outperforms the well-known combinatorial clock auction in a realistically-sized domain.

Figures (4)

• Figure 1: Auction phases of MLCA and iMLCA
• Figure 2: Illustration of Activity Rule \ref{['act:mrpar']}. We see the scenario before refinement in black. The upper bars are the upper bound utility $\overline{u}_i(x) = \overline{v}_i(x)-\pi(x)$, the lower bars are the lower bound utility $\underline{u} = \underline{v}_i(x) - \pi(x)$ and the dots are the true utility $u_i(x)$ induced by prices $\pi$. A bidder must refine their bounds such that the lower bound utility on their preferred bundle $x^{\ast}$ is at the same level as the upper bound utility on all their other bundles (illustrated in orange).
• Figure 3: Illustration of bundles that need not be considered by a bidder $i$ when responding to Activity Rule \ref{['act:mrpar']}. Shown is the scenario prior to refinement for given prices $\pi$. The bidder need not consider $x_{i1}$ and $x_{i2}$ as it is immediate from the location of the bounds that neither can be their preferred bundle.
• Figure 4: Comparison of the reported interval size distribution after the initialization phase and at the end of the auction.

Theorems & Definitions (16)

• Definition 1: Perturbed Valuation Lubin.2008
• Definition 2: $\delta$-approximate Clearing Prices At Reports
• Proposition 1: Individual Rationality
• proof
• Proposition 2: No-Deficit
• proof
• Definition 3: Truthful Strategy in iMLCA
• Proposition 3: Social Welfare Alignment
• proof
• Proposition 4: Truthful Reporting is an Ex-post Nash Equilibrium