How Does a Constant Product Market Maker (CPMM) Model Create Arbitrage Opportunities?

A CPMM, like the one used by Uniswap V2, maintains a constant product $x y = k$, where $x$ and $y$ are the quantities of the two assets in the pool. When a trade occurs, the ratio of $x$ and $y$ changes, which in turn changes the asset price.

If a trade on the CPMM causes the price to deviate from the price on other exchanges, an arbitrage opportunity is created. Arbitrageurs exploit this temporary price difference to profit and bring the pool's price back in line with the broader market.