Constant Function Market Making, Social Welfare and Maximal Extractable Value

Abstract: We consider the social welfare that can be facilitated by a constant function market maker (CFMM). When there is sufficient liquidity available to the CFMM, it can approximate the optimal social welfare when all users transactions are executed. When one of the agent has the role of proposing the block, and blockspace is scarce, they can obtain higher expected utility than otherwise identical agents. This gives a lower bound on the maximal extractable value exposed when blockspace is scarce.