Game Theoretic Analysis of Auction Mechanisms Modeled by Constrained Optimization Problems

This paper focuses on reverse auction mechanisms that may involve continuum values of different types of goods, general nonconvex constraints, and second stage costs. Our analysis seeks to address the payment rules and the conditions under which the coalitions of participants cannot influence the auction outcome in order to obtain higher collective utility. Under the dominant-strategy incentive-compatible VCG mechanism, coalition-proof outcomes are achieved if the derived conditions on the submitted bids and the constraint set are satisfied. By relaxing the property of incentive-compatibility, we investigate further payment rules that are coalition-proof, but without any extra conditions. Among the coalition-proof mechanisms, we pick the one that minimizes the participants’ ability to benefit from strategic manipulations in order to incentivize truthful bidding. Since calculating the payments for these mechanisms is computationally very 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.