Solving the Arctic Product-Mix Auction

Elizabeth Baldwin, Paul Klemperer and Edwin Lock

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Abstract: Arctic product-mix auctions allow budget-constrained bidders to express preferences over multiple substitute goods. We give the first strongly polynomial algorithm to find the competitive equilibria when the auctioneer has separable convex piecewise-linear costs. It combines a strongly polynomial reduction to the costless Arctic auction with an existing strongly polynomial algorithm for costless Arctic auctions. We also give a polynomial-time Turing reduction from costless Arctic auctions to linear Fisher markets, and a strongly polynomial many-to-one reduction to linear Arrow-Debreu exchange markets. If a good is sold in positive quantity in two competitive equilibria, its price is the same in both.

Date: 2026-09
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