FSS-CIMD seminar: Deciphering Equilibrium Behavior in First-Price Auction-Like Mechanisms
Speaker: Prof. Zenan WU, Professor, Department of Economics, School of Economics, Peking University
Date：28 May 2026 (Thu)
Time：16:00 – 17:15
Venue: E21B-G002
Abstract: Auction models serve as convenient abstractions for the free-form price-formation processes typical of decentralized markets. However, equilibrium analysis in such auction-like settings is challenging, as market frictions often cause participants’ bidding strategies to exhibit disconnected supports, non-monotonicity across types, or mass points. This paper develops a novel approach to equilibrium characterization in first-price auction-like mechanisms with a finite type space. Unlike the standard guess-and-verify approach that first posits equilibrium properties and then solves for bidding strategies, we reformulate the search for an equilibrium as a shooting problem: reducing the derivation of infinite-dimensional bidding strategies to finding a finite vector of equilibrium payoffs for each type that generates a path governed by the equilibrium conditions. We show that equilibrium existence is equivalent to the existence of a path that satisfies a simple regularity condition, allowing the equilibrium strategy profile to be recovered from this path—a property we term recoverability. Our approach thus bridges the literatures on equilibrium existence and characterization: proving existence simultaneously yields the bidding strategies. The recoverability condition can be guaranteed if the participants prefer winning to losing at their winning bids. We further leverage this insight to establish equilibrium existence for multi-unit pay-as-bid auctions with private values and possible loser forfeits, and multi-prize all-pay auctions with general value interdependence.
