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Liquidity and trading activity on constant function market makers (CFMMs)such as Uniswap, Curve, and Balancer has grown significantly in the second halfof 2020. Much of the growth of these protocols has been driven by incentivizedpools or 'yield farming', which reward participants in crypto assets forproviding liquidity to CFMMs. As a result, CFMMs and associated protocols,which were historically very small markets, now constitute the most liquidtrading venues for a large number of crypto assets. But what does it mean for aCFMM to be the most liquid market? In this paper, we propose a basic definitionof price sensitivity and liquidity. We show that this definition is tightlyrelated to the curvature of a CFMM's trading function and can be used toexplain a number of heuristic results. For example, we show that low-curvaturemarkets are good for coins whose market value is approximately fixed and thathigh-curvature markets are better for liquidity providers when traders have aninformational edge. Additionally, the results can also be used to modelinteracting markets and explain the rise of incentivized liquidity provision,also known as 'yield farming.'

When does the tail wag the dog? Curvature and market making