This article explores the theoretical limits of bidding mechanisms on blockchain and presents the impossibility theorem showing that no non-trivial truthful mechanism, whether deterministic or randomized, can simultaneously satisfy three key properties within a finite block size: User Incentive Compatibility (UIC), Miner Incentive Compatibility (MIC), and the Social Cost Property (SCP).
In the context of on-chain auctions and mechanisms, the UIC property requires that users do not increase their utility by lying about their valuations; MIC requires that miners cannot improve their profit by deviating from the order or inclusion of transactions; and SCP seeks to ensure that the resulting allocation minimizes global social cost. Applying Myerson's lemma and formal mechanism design arguments, it is demonstrated that any mechanism that guarantees full truthfulness for users and miners and also achieves a non-trivial social optimum conflicts with combinatorial constraints imposed by a finite block size.
Proof intuition: Myerson characterizes payments compatible with truthfulness through the monotonicity of the allocation rule and an integrated payment formula. In a blockchain environment with a limited block size, miners control the inclusion and order of transactions so that they can create profitable deviations if the allocation rule meets certain criteria. Avoiding such deviations would require degenerate allocation rules or infinitely large blocks. The formal result shows that any non-trivial mechanism becomes vulnerable to value extraction by the miner or loses user truthfulness.
Practical consequences: the theorem forces protocol designers to accept inevitable trade-offs. Among the viable paths are approximate mechanisms that guarantee truthfulness on average or with high probability, cryptographic restrictions such as sealed commitments that limit the miner's ability to manipulate, fee burning to reduce manipulation incentives, off-chain auctions to minimize miner control, or redesigned economic incentives that better align users and miners. None of these solutions completely eliminates the impossibility, but they provide useful mitigations according to specific needs.
Implications for adoption and governance: chains seeking fairness and efficiency should prioritize hybrid designs that combine protocol changes, off-chain solutions, and cryptographic auditing, as well as analysis tools to measure the incidence of deviations. Future research can quantify optimal approximations against finite block sizes and propose practical standards to minimize miner value extraction and social losses.
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