Designing Coalition-Proof Mechanisms for Auctions over Continuous Goods
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This paper investigates reverse auctions that involve continuous values of different types of goods, general nonconvex constraints, and second stage costs. Our analysis seeks to design the payment rules and conditions under which coalitions of participants cannot influence the auction outcome in order to obtain higher collective utility. Under incentive-compatible bidding in the Vickrey-Clarke-Groves mechanism, coalition-proof outcomes are achieved if the submitted bids are convex and the constraint sets are of polymatroid-type. Unfortunately, these conditions do not capture the complexity of the general class of reverse auctions under consideration. By relaxing the property of incentive-compatibility, we investigate further payment rules that are coalition-proof, but without any extra conditions. Among coalition-proof mechanisms, we select the mechanism that minimizes the participants' abilities to benefit from strategic manipulations, in order to incentivize truthful bidding from the participants. Since calculating the payments directly for these mechanisms is computationally difficult for auctions involving many participants, we present two computationally efficient methods. Our results are verified with several case studies based on electricity market data.
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