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