Constant Product Invariant

Definition ∞ The constant product invariant is a fundamental mathematical formula, typically expressed as x multiplied by y equals k, employed in automated market makers. This principle ensures that the product of the quantities of two assets within a liquidity pool remains constant, even as trades alter their individual balances. It governs the pricing mechanism, causing the price of one asset to increase as more of the other is added to the pool. This invariant underpins the functionality of many decentralized exchanges.
Context ∞ The constant product invariant is a critical component in the design and analysis of decentralized exchange liquidity pools. Its efficiency and limitations are frequently discussed in the context of slippage, impermanent loss, and arbitrage opportunities. Ongoing innovations in automated market maker design often seek to modify or extend this invariant to improve capital efficiency or reduce risks for liquidity providers. Grasping this concept is essential for comprehending how many digital asset trading platforms function.