Truthful, Credible, and Optimal Auctions for Matroids via Blockchains and Commitments

Abstract: We consider a revenue-optimizing auctioneer in single-dimensional environments with matroid feasibility constraints. Akbarpour and Li (2020) argue that any revenue-optimal, truthful, and credible mechanism requires unbounded communication. Recent works (Ferreira and Weinberg, 2020; Essaidi et al., 2022; Chitra et al., 2024) circumvent their impossibility for the single-item setting through the use of cryptographic commitments and blockchains. We extend their results to matroid feasibility constraints. At a high level, the two-round Deferred-Revelation Auction (DRA) discussed by Ferreira and Weinberg (2020) and Chitra et al., (2024) requires each bidder to submit a deposit, which is slashed upon presenting verifiable evidence indicating a deviation from the behaviour prescribed by the mechanism. We prove that the DRA satisfies truthfulness, credibility and revenue-optimality for all matroid environments when bidders' values are drawn from $\alpha$-strongly regular distributions for $\alpha > 0$. Further, we argue that the DRA is not credible for any feasibility constraint beyond matroids and for any smaller deposits than suggested by previous literature even in single-item environments. Finally, we modify the Ascending Deferred-Revelation Auction (ADRA) for single-item settings proposed by Essaidi et al., (2022) for arbitrary bidder value distributions. We implement a deferred-revelation variant of the deferred-acceptance auction for matroids due to Bikhchandani et al., (2011), which requires the same bounded communication as the ADRA.