Side-by-side first-price auctions with imperfect bidders
Benjamin Heymann
TL;DR
The paper analyzes side-by-side bidding where two imperfect bidders act for a single buyer in simultaneous first-price auctions, showing iterated best-response dynamics converge to a unique equilibrium under standard distributional assumptions. It adopts a model with multiplicative, stationary noise and log-concave distributions to capture learning and execution error, providing a tractable framework and numerical method for evaluating equilibrium outcomes. The results establish existence and uniqueness of equilibrium and explain how noise can influence the buyer's cost (e.g., winner's curse) while offering tools for practical analysis in ad-tech procurement. The approach yields theoretical insight and a practical methodology for studying two-agent procurement in markets with exogenous competition.
Abstract
We model a procurement scenario in which two \textit{imperfect} bidders act simultaneously on behalf of a single buyer, a configuration common in display advertising and referred to as \textit{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.