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 \emph{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.

翻译：恒定函数做市商（CFMMs），例如Uniswap，是一种在一组资产之间提供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——的技术关系。首先，我们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“良好”的做市商。随后，我们证明每个在$n$种资产上的此类CFMM等价于一个针对$n$种结果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激励公理，即市场擅长促进交易当且仅当它们擅长揭示信念。例如，我们证明每个CFMM隐含地定义了一个用于获取信念的\emph{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，我们的结果展示了预测市场和CFMMs的工具如何互操作。我们通过展示来自两个文献的流动性策略如何迁移到另一方来阐明这种互操作性，从而产生新的市场设计。