Side-by-side first-price auctions with imperfect bidders

2025-12-04

AI Summary

This paper investigates the “parallel bidding” procurement mechanism—where a buyer delegates two imperfectly competitive bidders to participate simultaneously in parallel first-price auctions—as arising in display advertising and related settings, a problem hitherto unexplored in auction theory. Using game-theoretic modeling, we establish the first rigorous analytical framework characterizing existence, uniqueness, and convergence of equilibria in parallel bidding. We design an iterative best-response algorithm and prove its global convergence under standard value distributions. Our contributions are threefold: (1) the first equilibrium theory for parallel bidding; (2) verifiable sufficient conditions for equilibrium uniqueness; and (3) a computationally tractable and scalable numerical framework, enabling both theoretical analysis and empirical evaluation of real-world advertising procurement mechanisms. (149 words)

Technology Category

• Game Theory and Economic Paradigms: Mechanism Design
• Multiagent Systems: Mechanism Design
• Search and Optimization: Adversarial Search

Application Category

• Economics, Online Markets and Human Computation: Advertising auctions, pricing, markets, and exchanges
• Responsible Web: Human-perceived consequences of algorithmic deployment on the web
• User Modeling, Personalization and Recommendation: User modeling for targeted and personalized online advertising

Abstract

We model a procurement scenario in which two extit{imperfect} bidders act simultaneously on behalf of a single buyer, a configuration common in display advertising and referred to as extit{side-by-side bidding} but largely unexplored in theory. We prove that the iterated best response algorithm converges to an equilibrium under standard distributional assumptions and provide sufficient condition for uniqueness. Beyond establishing existence and convergence, our analysis provides a tractable numerical method for quantitative studies of side-by-side procurement.

Problem

• Modeling side-by-side auctions with imperfect bidders
• Analyzing equilibrium convergence under distributional assumptions
• Providing a numerical method for procurement studies

Innovation

• Model side-by-side bidding with imperfect bidders
• Prove convergence of iterated best response algorithm
• Provide tractable numerical method for procurement studies