  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.
