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A Note on Optimal Fees for Constant Function Market Makers


  • Robin Fritsch
  • Roger Wattenhofer


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.

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  • Robin Fritsch & Roger Wattenhofer, 2021. "A Note on Optimal Fees for Constant Function Market Makers," Papers 2105.13510,
  • Handle: RePEc:arx:papers:2105.13510

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    References listed on IDEAS

    1. Guillermo Angeris & Alex Evans & Tarun Chitra, 2020. "When does the tail wag the dog? Curvature and market making," Papers 2012.08040,
    2. Alex Evans & Guillermo Angeris & Tarun Chitra, 2021. "Optimal Fees for Geometric Mean Market Makers," Papers 2104.00446,
    3. Alex Evans, 2020. "Liquidity Provider Returns in Geometric Mean Markets," Papers 2006.08806,, revised Jul 2020.
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