Mathematical Finance (q-fin.MF)

Abstract: We develop a formalism for reasoning about trading on decentralized exchanges on blockchains and a formulation of a particular form of maximal extractable value (MEV) that represents the total arbitrage opportunity extractable from on-chain liquidity. We use this formalism to prove that for blockchains with deterministic block times whose liquidity pools satisfy some natural properties that are satisfied by pools in practice, this form of MEV is invariant under changes to the ordering mechanism of the blockchain and distribution of block times. We do this by characterizing the MEV as the profit of a particularly simple arbitrage strategy when left uncontested. These results can inform design of blockchain protocols by ruling out designs aiming to increase trading opportunity by changing the ordering mechanism or shortening block times.