What Is an Arbitrageur’s Role in Maintaining the X Y=k Constant in an AMM?

Arbitrageurs are essential actors who ensure the pool's internal price ratio, determined by x/y, remains synchronized with the external market price. When the external price deviates from the pool's price, arbitrageurs profit by trading with the pool until the prices align.

For example, if the token is cheaper in the pool, they buy it from the pool and sell it on the external exchange for a profit. This trading activity rebalances the x and y reserves, keeping the pool on the x y=k curve and correcting the price.