Optimal linear-payment auction design with aftermarket collaboration

2026-04-20

AI Summary

This study addresses the dual problems of moral hazard and adverse selection arising from non-contractible collaborative efforts between a seller and the winning bidder following an auction. By constructing a linear payment mechanism that combines fixed cash transfers with proportional value sharing, the paper designs optimal direct mechanisms under two collaboration structures—winner-led and seller-led—to maximize virtual surplus and induce truthful type revelation. Drawing on mechanism design theory, virtual surplus analysis, and a dual moral hazard framework, the analysis demonstrates that the seller-led structure strictly dominates the winner-led one: it not only enables implementation via a standard ascending auction with full type disclosure and deterministic allocation but also substantially increases the seller’s expected revenue, even driving the surplus of low-type winners to zero.

Technology Category

Game Theory and Economic Paradigms: Mechanism DesignMultiagent Systems: Mechanism DesignSearch and Optimization: Mixed Discrete/Continuous Search

Application Category

Economics, Online Markets and Human Computation: Uses of LLMs and GenAI for marketplace design, bidding, and strategic interactionsUser Modeling, Personalization and Recommendation: Accountability, Transparency, and Ethics for personalizationSecurity and Privacy: Data transparency and provenance

Abstract

This paper studies optimal auction design when valuations depend endogenously on post-auction collaboration between the seller and the winning bidder. Both parties exert non-contractible efforts after the auction, generating a double moral hazard problem alongside adverse selection. We analyze two role structures -- winner-pivotal and seller-pivotal collaboration -- and characterize optimal direct mechanisms using linear payment schemes that combine cash transfers with proportional value sharing. The optimal mechanism allocates the asset to the bidder with the highest virtual surplus, employs a deterministic value-sharing rule, and achieves full type revelation through the signal realization rule. Comparing the two scenarios yields three main findings. First, regarding value sharing, the seller secures a strictly higher share under seller-pivotal collaboration: for sufficiently low-type winners, the seller extracts the entire value, whereas under winner-pivotal collaboration every winner must retain a positive share to sustain his critical effort. Second, regarding effort exertion, the pivotal party always exerts higher post-auction effort than the supporting party, and each party exerts greater effort when pivotal than when providing support. Third, seller-pivotal collaboration yields strictly higher seller revenue than winner-pivotal collaboration for any type distribution. Finally, these optimal mechanisms can be implemented through ascending auctions with endogenously determined linear contracts.

Problem

• optimal auction design
• aftermarket collaboration
• double moral hazard
• adverse selection
• linear payment

Innovation

• optimal auction design
• aftermarket collaboration
• double moral hazard
• linear payment scheme
• virtual surplus