Blockchains have popularized the Automated Market Makers (AMMs), where users trade crypto-assets directly with a smart contract, governed by a pricing function embedded in the contract's code. Today, users of AMMs are often forced to accept unfavorable prices due to widespread front-running and back-running attacks, commonly known as Miner Extractable Value (MEV). Several earlier works show impossibility results suggesting that completely removing MEV at the consensus layer is impossible, partly because the consensus layer is agnostic of application-level semantics. For this reason, more recent works have advocated mechanism design approaches at the application (i.e., smart contract) level. We study a natural two-asset AMM mechanism design problem recently initiated and explored in prior work by Chan, Wu, and Shi, in which they proposed a mechanism that satisfies a surprisingly strong notion of incentive compatibility (IC), under the consensus assumption that the underlying blockchain provides sequencing fairness. In this paper, we investigate the (in)feasibility of simultaneously achieving IC and other desirable properties such as weak local efficiency (wLE) and uniform pricing (UP). At a high level, wLE requires that the mechanism should not leave any unfulfilled demand from users whose asking prices are not overly restrictive, and whose orders could have been executed directly against the pool. UP requires that all orders that get (partially) executed must trade at the same exchange rate. We unveil the underlying mathematical structure of AMM mechanism design, and our main results can be summarized as a trilemma-style theorem: among the desirable properties IC, wLE, and UP, any two out of three are possible, but no mechanism can satisfy all three.

翻译：区块链技术使得自动做市商（AMMs）得以普及，用户通过嵌入合约代码的定价函数直接与智能合约交易加密资产。目前，由于广泛存在的抢先交易与尾随攻击（通常被称为矿工可提取价值MEV），AMM用户往往被迫接受不利的定价。多项早期研究指出不可能性结果，表明在共识层完全消除MEV是不可能的，部分原因在于共识层对应用层语义不具有感知能力。为此，近期研究更倾向于在应用层（即智能合约层面）采用机制设计方法。我们研究了Chan、Wu和Shi在先前工作中提出并探索的一个自然的两资产AMM机制设计问题——该机制在底层区块链提供排序公平性的共识假设下，实现了出人意料的强激励相容性（IC）属性。本文探究同时实现IC及其他理想属性（如弱局部效率wLE和统一定价UP）的可行性。在较高层面上，wLE要求机制不应留下任何来自报价不过于严苛且订单可直接与流动性池执行的用户需求缺口；UP要求所有被（部分）执行的订单必须以相同汇率交易。我们揭示了AMM机制设计的底层数学结构，主要结论可概括为三元悖论式定理：在IC、wLE和UP这三个理想属性中，任意两者均可同时实现，但不存在能同时满足三者的机制。