A Faster Algorithm for Bidder-Optimal Core Points

In complex combinatorial markets with complementary valuations, truthful auctions can yield low revenue. Core-selecting auctions attempt to boost revenue by setting prices so that no group of agents, including the auctioneer, can jointly improve their utilities by switching to a different allocation and payments. Among outcomes in the core, bidder-optimal core points have been the most widely studied due to their incentive properties, such as being implementable at equilibrium. Prior work in economics has studied heuristics and algorithms for computing approximate bidder-optimal core points given oracle access to the welfare optimization problem, but these solutions either lack performance guarantees or are based on prohibitively expensive convex programs. Our main result is a combinatorial algorithm that finds an approximate bidder-optimal core point in a quasi-linear number of calls to the welfare maximization oracle.