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

2025-07-06

AI Summary

This paper addresses the challenge of simultaneously achieving revenue optimality, truthfulness, and verifiability under matroid feasibility constraints in single-dimensional auctions—a problem for which Akbarpour & Li (2020) established an impossibility result under infinite communication. We propose a two-round Delayed Revelation Auction (DRA) and its ascending variant (ADRA), leveraging blockchain infrastructure and cryptographic commitment schemes. Under α-strongly regular value distributions, we rigorously prove that both mechanisms satisfy incentive compatibility, verifiability (i.e., tamper-proof on-chain verification), and asymptotically optimal revenue. To our knowledge, this is the first work to systematically integrate distributed ledger technology and cryptographic commitments into matroid-constrained auction design, achieving all three properties with bounded communication complexity. Furthermore, we extend ADRA to arbitrary value distributions while preserving low communication overhead. Our results broaden the theoretical foundations and practical applicability of delayed revelation mechanisms to multi-dimensional feasible domains.

Technology Category

• Multiagent Systems: Mechanism Design
• Game Theory and Economic Paradigms: Mechanism Design
• Constraint Satisfaction and Optimization: Distributed CSP/Optimization

Application Category

• Security and Privacy: Blockchains and distributed ledgers
• Economics, Online Markets and Human Computation: Economic aspects of blockchain and cryptocurrencies
• Responsible Web: Data and user privacy-enhancing technologies for the Web

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 $α$-strongly regular distributions for $α> 0$. 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.

Problem

• Extend truthful credible auctions to matroid constraints
• Ensure revenue-optimality with cryptographic commitments
• Modify auctions for arbitrary bidder value distributions

Innovation

• Uses blockchain for credible auctions
• Implements two-round Deferred-Revelation Auction
• Modifies ADRA for arbitrary distributions