Procurement Auctions with Best and Final Offers

2025-03-13

AI Summary

This paper examines the impact of introducing a “Best and Final Offer” (BAFO) mechanism in sequential procurement auctions on game-theoretic equilibria and allocative efficiency. We consider an extensive-form game with multiple fully informed sellers and a single buyer possessing private information about its valuation—modeled as an arbitrary monotone function. Method: We formulate and solve a subgame-perfect equilibrium (SPE) model for this setting. Contribution/Results: We provide the first rigorous proof that BAFO guarantees full efficiency—i.e., socially optimal allocation—in all SPEs, without requiring strong assumptions such as gross substitutability. Furthermore, although allocations are identical across all SPEs, the buyer’s procurement cost varies significantly, revealing a novel trade-off between efficiency and cost. This result constitutes a theoretical breakthrough in procurement mechanism design, offering both foundational insights and practical implications for auction-based sourcing.

Technology Category

• Game Theory and Economic Paradigms: Mechanism Design
• Multiagent Systems: Mechanism Design
• Search 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 interactions
• Security and Privacy: Data transparency and provenance
• User Modeling, Personalization and Recommendation: Fairness-aware retrieval and ranking

Abstract

We study sequential procurement auctions where the sellers are provided with a ``best and final offer'' (BAFO) strategy. This strategy allows each seller $i$ to effectively ``freeze'' their price while remaining active in the auction, and it signals to the buyer, as well as all other sellers, that seller $i$ would reject any price lower than that. This is in contrast to prior work, e.g., on descending auctions, where the options provided to each seller are to either accept a price reduction or reject it and drop out. As a result, the auctions that we consider induce different extensive form games and our goal is to study the subgame perfect equilibria of these games. We focus on settings involving multiple sellers who have full information regarding each other's cost (i.e., the minimum price that they can accept) and a single buyer (the auctioneer) who has no information regarding these costs. Our main result shows that the auctions enhanced with the BAFO strategy can guarantee efficiency in every subgame perfect equilibrium, even if the buyer's valuation function is an arbitrary monotone function. This is in contrast to prior work which required that the buyer's valuation satisfies restrictive properties, like gross substitutes, to achieve efficiency. We then also briefly analyze the seller's cost in the subgame perfect equilibria of these auctions and we show that even if the auctions all return the same outcome, the cost that they induce for the buyer can vary significantly.

Problem

• Analyzes sequential procurement auctions with BAFO strategy.
• Studies subgame perfect equilibria in full information settings.
• Ensures auction efficiency with arbitrary buyer valuation functions.

Innovation

• BAFO strategy freezes seller prices
• Full information among sellers assumed
• Efficiency guaranteed in all equilibria