Trade-intent auctions intermediate around USD~9~billion in monthly trading volume. In these auctions, specialized intermediaries called solvers compete for the right to execute orders across fragmented blockchain-based financial markets. These auctions are combinatorial because executing multiple trade intents jointly generates additional efficiencies. However, there is no best-execution benchmark to determine how to share those efficiencies: the best possible execution of a trade is solvers' private information and must be elicited. We study theoretically the two main mechanisms: batch auctions, in which a group of trades is auctioned off jointly, and independent trade-by-trade auctions. Batch auctions return more total value to traders, but their outcome may be unfair, in the sense of leaving one trader worse off than under independent auctions. We propose a fair combinatorial auction: solvers bid on individual trades and on batches of trades, but a batched bid is filtered out if any trader earns less than an execution benchmark constructed from the bids on individual trades and a counterfactual mechanism. Whether fairness guarantees arise in equilibrium depends on the counterfactual mechanism: independent first-price auctions generate such guarantees; independent second-price auctions do not. These fairness guarantees come at a cost: a lower total value returned to traders.

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