CFMM的公理化刻画及其与预测市场的等价性
An Axiomatic Characterization of CFMMs and Equivalence to Prediction Markets
AI总结：
本文研究了CFMM与成本函数预测市场的等价关系，证明具有凹势函数的CFMM满足做市商公理且可转换为预测市场，揭示了促进交易与揭示信念的等价性，并展示了两者工具的互操作性。
摘要：
恒定函数做市商（CFMMs，如Uniswap）是提供一组资产间交易的自动化交易所。我们研究了它们与另一类自动化做市商——成本函数预测市场之间的技术关系。我们首先引入了做市商的公理，并证明具有凹势函数的CFMMs根据这些公理刻画了“好”的做市商。然后证明，任何此类关于$n$种资产的CFMM都等价于具有$n$个结果的事件的成本函数预测市场。我们的构造直接将CFMM转换为预测市场，反之亦然。从概念上讲，我们的结果表明，理想的做市公理等价于理想的信息获取公理，即市场善于促进交易当且仅当它善于揭示信念。例如，每个CFMM隐式定义了一个用于获取信念的适当评分规则；Uniswap的评分规则虽不寻常但已知。从技术角度看，结果表明预测市场和CFMMs的工具可以互操作。我们通过展示两篇文献中的流动性策略如何相互转移，从而产生新的市场设计，来说明这种互操作性。
英文摘要：
Constant-function market makers (CFMMs), such as Uniswap, are automated exchanges offering trades among a set of assets. We study their technical relationship to another class of automated market makers, cost-function prediction markets. We first introduce axioms for market makers and show that CFMMs with concave potential functions characterize "good" market makers according to these axioms. We then show that every such CFMM on $n$ assets is equivalent to a cost-function prediction market for events with $n$ outcomes. Our construction directly converts a CFMM into a prediction market and vice versa. Conceptually, our results show that desirable market-making axioms are equivalent to desirable information-elicitation axioms, i.e., markets are good at facilitating trade if and only if they are good at revealing beliefs. For example, we show that every CFMM implicitly defines a proper scoring rule for eliciting beliefs; the scoring rule for Uniswap is unusual, but known. From a technical standpoint, our results show how tools for prediction markets and CFMMs can interoperate. We illustrate this interoperability by showing how liquidity strategies from both literatures transfer to the other, yielding new market designs.
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