Table of Links Abstract and 1. Introduction Abstract and 1. Introduction 1.1 Our Contributions 1.1 Our Contributions 1.2 TFM Incentive-Compatibility Notions: A Cheat Sheet 1.2 TFM Incentive-Compatibility Notions: A Cheat Sheet Definitions
2.1 Transaction Fee Mechanism
2.2 Incentive Compatibility Notions


Preliminary: Myerson’s Lemma


Warmup: Impossibility of UIC + MIC + Global SCP for Deterministic Mechanisms


Impossibility of UIC + MIC + Global SCP for Randomized Mechanisms and 5.1 Proof Roadmap
5.2 Formal Proofs


Feasibility and Impossibility of UIC + MIC + OCA-Proof
6.1 A Non-Truthful Mechanism with UIC + MIC + OCA-Proof
6.2 Impossibility of UIC + MIC + OCA-Proof for Truthful Mechanisms


How to Circumvent the Impossibilities and 7.1 Allowing the Globally Optimal Strategy to Coordinate
7.2 Allowing the Globally Optimal Strategy to Output Multiple Bids
7.3 Inclusion-Rule-Respecting and 7.4 Discussions and Open Questions Regarding the Use of Cryptography


Static Revelation Principle for Transaction Fee Mechanisms
8.1 Static Revelation Principle: Bidding Rules That Output Single Bid
8.2 Static Revelation Principle: Allowing Bidding Rules that Output Multiple Bids Definitions
2.1 Transaction Fee Mechanism
2.2 Incentive Compatibility Notions Definitions 2.1 Transaction Fee Mechanism 2.1 Transaction Fee Mechanism 2.2 Incentive Compatibility Notions 2.2 Incentive Compatibility Notions Preliminary: Myerson’s Lemma Preliminary: Myerson’s Lemma Preliminary: Myerson’s Lemma Warmup: Impossibility of UIC + MIC + Global SCP for Deterministic Mechanisms Warmup: Impossibility of UIC + MIC + Global SCP for Deterministic Mechanisms Warmup: Impossibility of UIC + MIC + Global SCP for Deterministic Mechanisms Impossibility of UIC + MIC + Global SCP for Randomized Mechanisms and 5.1 Proof Roadmap
5.2 Formal Proofs Impossibility of UIC + MIC + Global SCP for Randomized Mechanisms and 5.1 Proof Roadmap Impossibility of UIC + MIC + Global SCP for Randomized Mechanisms and 5.1 Proof Roadmap 5.2 Formal Proofs 5.2 Formal Proofs Feasibility and Impossibility of UIC + MIC + OCA-Proof
6.1 A Non-Truthful Mechanism with UIC + MIC + OCA-Proof
6.2 Impossibility of UIC + MIC + OCA-Proof for Truthful Mechanisms Feasibility and Impossibility of UIC + MIC + OCA-Proof Feasibility and Impossibility of UIC + MIC + OCA-Proof 6.1 A Non-Truthful Mechanism with UIC + MIC + OCA-Proof 6.1 A Non-Truthful Mechanism with UIC + MIC + OCA-Proof 6.2 Impossibility of UIC + MIC + OCA-Proof for Truthful Mechanisms 6.2 Impossibility of UIC + MIC + OCA-Proof for Truthful Mechanisms How to Circumvent the Impossibilities and 7.1 Allowing the Globally Optimal Strategy to Coordinate
7.2 Allowing the Globally Optimal Strategy to Output Multiple Bids
7.3 Inclusion-Rule-Respecting and 7.4 Discussions and Open Questions Regarding the Use of Cryptography How to Circumvent the Impossibilities and 7.1 Allowing the Globally Optimal Strategy to Coordinate How to Circumvent the Impossibilities and 7.1 Allowing the Globally Optimal Strategy to Coordinate 7.2 Allowing the Globally Optimal Strategy to Output Multiple Bids 7.2 Allowing the Globally Optimal Strategy to Output Multiple Bids 7.3 Inclusion-Rule-Respecting and 7.4 Discussions and Open Questions Regarding the Use of Cryptography 7.3 Inclusion-Rule-Respecting and 7.4 Discussions and Open Questions Regarding the Use of Cryptography Static Revelation Principle for Transaction Fee Mechanisms
8.1 Static Revelation Principle: Bidding Rules That Output Single Bid
8.2 Static Revelation Principle: Allowing Bidding Rules that Output Multiple Bids Static Revelation Principle for Transaction Fee Mechanisms Static Revelation Principle for Transaction Fee Mechanisms 8.1 Static Revelation Principle: Bidding Rules That Output Single Bid 8.1 Static Revelation Principle: Bidding Rules That Output Single Bid 8.2 Static Revelation Principle: Allowing Bidding Rules that Output Multiple Bids 8.2 Static Revelation Principle: Allowing Bidding Rules that Output Multiple Bids A. Comparison of Collusion-Resilience Notions A. Comparison of Collusion-Resilience Notions References References A Comparison of Collusion-Resilience Notions Lemma A.1. The even auction above satisfies global SCP but not OCA-proofness. Lemma A.1. The even auction above satisfies global SCP but not OCA-proofness. Notice that whether the individually rational bidding strategy σ outputs a single bid or multiple bids is important. If we require σ to only output a single real as we defined in Definition 6, there is no non-trivial TFM that can satisfy UIC, MIC, and OCA-proofness as we proved in Theorem 6.9. However, if we allow σ to output multiple bids, we obtain a feasibility in Section 7.2. When we analyze whether a TFM satisfies c-SCP for some c, 1-SCP is the weakest requirement since c′ -SCP always implies c-SCP for any c′ > c by definition. Interestingly, even so, 1-SCP is incomparable with global SCP and OCA-proofness. The relations between 1-SCP, global SCP, and OCA-proofness is depicted in Figure 1. We explain Figure 1 in more detail below: Below, we introduce the (somewhat contrived) auctions for constructing the counterexamples. Lemma A.2. The pay-nothing auction above satisfies global SCP and OCA-proofness. However, it does not satisfy 1-SCP. Lemma A.2. The pay-nothing auction above satisfies global SCP and OCA-proofness. However, it does not satisfy 1-SCP. Lemma A.3. The discount auction above satisfies 1-SCP. However, it does not satisfy global SCP or OCA-proofness. Lemma A.3. The discount auction above satisfies 1-SCP. However, it does not satisfy global SCP or OCA-proofness. Now, we show that the mechanism does not satisfy OCA-proofness. Imagine a scenario where there are 10 users each with the true value r. Without injecting any fake bid, the lowest possible payment for each user is f(10) = r, so the social welfare is at most 0. However, if the global coalition inject one fake bid r, everyone’s payment will further lower to f(11) = r/2. In this case, the social welfare becomes 10r − 11r/2 = 9r/2 > 0. Thus, the mechanism does not satisfy OCA-proofness. The mechanism does not satisfy global SCP either since the bidding rule only outputs a single real. If the mechanism satisfied global SCP, the global coalition could pick the suggested bidding rule as the individually rational bidding strategy σ to maximize the social welfare. 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[WAS22] Ke Wu, Gilad Asharov, and Elaine Shi. A complete characterization of gametheoretically fair, multi-party coin toss. In Eurocrypt, 2022. [WSC24] Ke Wu, Elaine Shi, and Hao Chung. Maximizing Miner Revenue in Transaction Fee Mechanism Design. In Venkatesan Guruswami, editor, 15th Innovations in Theoretical Computer Science Conference (ITCS 2024), 2024. [XFP23] Matheus Venturyne Xavier Ferreira and David C Parkes. Credible decentralized exchange design via verifiable sequencing rules. In Proceedings of the 55th Annual ACM Symposium on Theory of Computing, pages 723–736, 2023. [Yao] Andrew Chi-Chih Yao. An Incentive Analysis of Some Bitcoin Fee Designs (Invited Talk). In ICALP 2020. [ZCZ22] Zishuo Zhao, Xi Chen, and Yuan Zhou. Bayesian-nash-incentive-compatible mechanism for blockchain transaction fee allocation. https://arxiv.org/abs/2209.13099, 2022. Authors:
(1) Hao Chung∗, Carnegie Mellon University (haochung@andrew.cmu.edu);
(2) Tim Roughgarden†, Columbia University and a16z (crypto tim.roughgarden@gmail.com);
(3) Elaine Shi∗, Carnegie Mellon University (runting@cs.cmu.edu). Authors: Authors: (1) Hao Chung∗, Carnegie Mellon University (haochung@andrew.cmu.edu); (2) Tim Roughgarden†, Columbia University and a16z (crypto tim.roughgarden@gmail.com); (3) Elaine Shi∗, Carnegie Mellon University (runting@cs.cmu.edu). This paper is available on arxiv under CC BY 4.0 DEED license. This paper is available on arxiv under CC BY 4.0 DEED license. available on arxiv available on arxiv

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