Combinatorial Auctions without a Numeraire: The Case of Blockchain Trade-Intent Auctions

Blockchain trade intent auctions currently intermediate approximately USD 5 billion monthly. Due to production complementarities, the auction is combinatorial: when multiple trade intents from different traders are auctioned off simultaneously, a bidder (here called solver) can generate additional efficiencies by winning a batch of multiple trade intents. However, unlike other combinatorial auctions studied in the literature, the auction has no numeraire. Fairness is a concern as the efficiencies from batching cannot be easily shared between traders. We formalize this problem and study the most commonly used auction formats: batch auctions and multiple simultaneous auctions. We also propose a novel fair combinatorial auction that combines batch auction and multiple simultaneous auctions: solvers submit individual-trade bids and batched bids, but batched bids are considered only if they are better for all traders relative to the outcome of multiple simultaneous auctions (constructed using the individual-trade bids). We find a trade-off between the fairness guarantees provided by the auction (i.e., the minimum each trader can expect to receive) and the expected value of the assets returned to the traders. Also, the amount that each trader receives in the equilibrium of the fair combinatorial auction may be higher or lower than what they receive in the equilibrium of the simultaneous auctions used as a benchmark for fairness.