We are interested in how the relationship between the fee in constant a product market (CPM) 
    and the volatility of the swapped pair on other liquid exchanges influences the losses / gains 
    of the liquidity providers. We review three classical market making models: Glosten and
    Milgrom, Kyle and Grossman and Miller and note that these very different models there is always 
    a relationship between volatility and how rational market makers set prices. Motivated by this 
    we set up an agent based model to explore this in the con- text of CPMs like Uniswap. 
    We conclude that if the fee is too low relative to the volatility of the traded pair then the 
    liquidity providers will end up making a loss over the medium term. From this we go to suggesting that 
    CPM markets need to let liquidity providers set the fee via a governance mechanism especially as 
    volatilities of assets fluctuate. The code for all simulations is available at https://github.com/kGFRqao2/cpmagentbasedsim.