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:诸如 Uniswap 等常态市场制造者(CFMM) 等常态市场制造者(CFMM) 是一系列资产之间的自动交换交易。 我们研究它们与另一类自动市场制造者的技术关系, 成本- 功能预测市场。 我们首先为市场制造者引入轴心, 并显示具有共性潜在功能的CFMM公司根据这些轴心对“ 良好” 市场制造者具有“ 良好” 的特性。 我们然后显示, 美元资产上的每个CFMM公司都相当于以美元计算结果的事件的成本- 预测市场。 我们的建设直接将CFMM公司转换为预测市场,反之则相反。 从技术上看, 我们的结果显示, 理想的市场制造轴心与理想的信息- 引用轴心, 也就是说, 市场在便利贸易方面是良好的, 只有当它们根据这些轴心, 能够根据这些轴心显示, 我们显示, 每个CFMMMM公司都暗中定义了获取信念的成本-emph{ press 评分规则; 规则是不寻常的, 但是我们知道, 我们的评分规则是不寻常的。 从技术角度, 我们的结果表明, 我们的结果显示, 如何预测市场和CFMMSMS 之间如何显示, 从新的流动性转换。