The Groupwise-Pivotal Referral Mechanism: Core-Selecting Referral Strategy-Proof Mechanism

Abstract

We introduce the groupwise-pivotal referral (GPR) mechanism for auctions where buyers can participate only through referrals. Each buyer's type consists of a valuation and referable buyers. Unlike the second-price auction (SPA), the Vickrey-Clarke-Groves (VCG) mechanism provides referral incentives. However, VCG is not budget-feasible. In contrast, GPR is core-selecting, implying efficiency and budget feasibility. In GPR, bidders should refer truthfully and have no incentive to underbid. GPR is shill-proof and groupwise collusion-proof. Furthermore, GPR's ex-post revenue outperforms both VCG and SPA in undominated strategies. We also study more general environments than auctions.