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.
翻译:常函数市场制造者(CFMMs),例如Uniswap,是自动化交易所,提供一组资产的交易。我们研究它们与另一类自动化市场制造者,成本函数预测市场的技术关系。我们首先引入了市场制造者的公理并表明具有凸势能函数的CFMMs符合这些公理的“好市场制造者”的特性。然后,我们展示了每个具有$n$个资产的CFMM都等价于一个$n$个结果的事件成本函数预测市场。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,有利于市场制造的公理与有利于信息引导的公理是等价的,即如果市场能够很好地揭示信仰,那么市场就能够很好地促进交易。例如,我们展示了每个CFMM隐含地定义了一种适当的记分规则以引导信仰;Uniswap的记分规则是不寻常的,但已知。从技术的角度来看,我们的结果展示了预测市场和CFMMs的工具如何相互运作。我们通过展示两个文献中的流动性策略如何互相转移,从而得到新的市场设计,来说明这种互操作性。