Communication and Correlated Equilibria in First-Price Auctions

Abstract

We explore the question of collusion through communication in first-price auctions, asking whether there exist any collusive equilibria with higher bidder surplus than the Nash equilibrium. We show that the set of collusive equilibria in first-price auctions is strictly smaller than in second-price auctions. We apply linear programming techniques to the problem of finding collusive equilibria, considering both communication equilibrium and Bayes correlated equilibrium as solution concepts. We also consider the Lagrange relaxation of these programs, a dual optimization problem which bounds their results. We approximate these programs numerically and make several observations about the structure of their solutions