We suggest a framework to determine optimal trading fees for constant function market makers (CFMMs) in order to maximize liquidity provider returns. In a setting of multiple competing liquidity pools, we show that no race to the bottom occurs, but instead pure Nash equilibria of optimal fees exist. We theoretically prove the existence of these equilibria for pools using the constant product trade function used in popular CFMMs like Uniswap. We also numerically compute the equilibria for a number of examples and discuss the effects the equilibrium fees have on capital allocation among pools. Finally, we use our framework to compute optimal fees for real world pools using past trade data.

翻译：我们建议建立一个框架,确定固定功能市场制造者的最佳交易费,以便最大限度地提高流动性提供者的回报率。 在多个相互竞争的流动性池的环境下,我们显示没有发生竞争,而是存在纯粹的纳什最佳收费平衡。我们理论上证明,在使用Uniswap等流行的CFMMs中所使用的固定产品贸易功能的集合方面,存在着这种平衡。我们还用数字计算一些例子的平衡,并讨论平衡费用对集合之间资本分配的影响。最后,我们利用我们的框架用过去的贸易数据计算真实世界集合的最佳费用。