The paper explores the design of transaction fee mechanisms (TFMs) in cryptocurrencies, focusing on collusion resistance. It addresses the conjecture by Roughgarden [Rou21] that there exists a TFM that is both incentive-compatible for users and miners (DSIC and MMIC) and resistant to off-chain agreements (OCAs). Chung and Shi [CS23] introduced the concept of side-channel proofness (SCP), a notion of collusion resistance, and showed that achieving DSIC and SCP simultaneously is impossible. The authors of this paper demonstrate that OCA-proofness and SCP are distinct, with SCP being strictly stronger. They fully characterize the intersection of deterministic DSIC and OCA-proof mechanisms, as well as deterministic MMIC and OCA-proof mechanisms, and conclude that only the trivial mechanism satisfies these properties. For randomized mechanisms, they show that the trivial mechanism is the only DSIC, MMIC, and OCA-proof mechanism that is scale-invariant, and bound the efficiency of such mechanisms to at most 0.842 in the worst case. The paper also discusses the dynamic setting and the trade-offs between randomized and deterministic mechanisms, highlighting the challenges of implementing randomness in blockchain settings.The paper explores the design of transaction fee mechanisms (TFMs) in cryptocurrencies, focusing on collusion resistance. It addresses the conjecture by Roughgarden [Rou21] that there exists a TFM that is both incentive-compatible for users and miners (DSIC and MMIC) and resistant to off-chain agreements (OCAs). Chung and Shi [CS23] introduced the concept of side-channel proofness (SCP), a notion of collusion resistance, and showed that achieving DSIC and SCP simultaneously is impossible. The authors of this paper demonstrate that OCA-proofness and SCP are distinct, with SCP being strictly stronger. They fully characterize the intersection of deterministic DSIC and OCA-proof mechanisms, as well as deterministic MMIC and OCA-proof mechanisms, and conclude that only the trivial mechanism satisfies these properties. For randomized mechanisms, they show that the trivial mechanism is the only DSIC, MMIC, and OCA-proof mechanism that is scale-invariant, and bound the efficiency of such mechanisms to at most 0.842 in the worst case. The paper also discusses the dynamic setting and the trade-offs between randomized and deterministic mechanisms, highlighting the challenges of implementing randomness in blockchain settings.