Open vs. Sealed: Auction Format Choice for Maximal Extractable Value

We study optimal auction design for Maximum Extractable Value (MEV) auction markets on Ethereum. Using a dataset of 2.2 million transactions across three major orderflow providers, we establish three empirical regularities: extracted values follow a log-normal distribution with extreme right-tail concentration, competition intensity varies substantially across MEV types, and the standard Revenue Equivalence Theorem breaks down due to affiliation among searchers' valuations. We model this affiliation through a Gaussian common factor, deriving equilibrium bidding strategies and expected revenues for five auction formats, first-price sealed-bid, second-price sealed-bid, English, Dutch, and all-pay, across a fine grid of bidder counts $n$ and affiliation parameters $\rho$. Our simulations confirm the Milgrom-Weber linkage principle: English and second-price sealed-bid auctions strictly dominate Dutch and first-price sealed-bid formats for any $\rho > 0$, with a linkage gap of 14-28\% at moderate affiliation ($\rho=0.5$) and up to 30\% for small bidder counts. Applied to observed bribe totals, this gap corresponds to \$10-18 million in foregone revenue over the sample period. We also document a novel non-monotonicity: at large $n$ and high $\rho$, revenue peaks in the interior of the affiliation parameter space and declines thereafter, as near-perfect correlation collapses the order-statistic spread that drives competitive payments.