Cartels and bidding rings are often facilitated by intermediaries, who recommend prices/bids to firms and can impose penalties (such as reverting to competitive behavior in future interactions) if these recommendations are not followed. Motivated by such cases, we study correlated equilibria in first-price procurement auctions with complete information, where bidders who disobey their recommendations are penalized. Cartel-optimal profit is greater when more information about submitted bids is disclosed at auction and when the maximum penalty is larger. When only the winner's identity is disclosed (or the winner's identity and bid), cartels do not benefit from mediation. Our main result characterizes the cartel-optimal equilibrium with two symmetric bidders when both bids are disclosed. The optimal equilibrium involves extensive randomization and displays tied bids and high winning bids with positive probability, even when the maximum penalty is very small. The stationary mediation schemes we consider are always more profitable for the cartel than bid rotation.
