Collusion with Private Monitoring and Private Information

Abstract

We consider a model of price competition and collusion with private monitoring. The sellers have homogeneous good, and the buyer has a unit demand every period over an infinite horizon. The buyer's valuation is his private information, and the sellers start with a common prior. The seller only knows when the buyer comes to him and what price he charges. The buyer knows the price of the seller he visits. We characterize sequential equilibria and focus on equilibria that maximize the sellers' payoffs. When the sellers know the buyer's valuation, the buyer's payoff can be any number between his outside option and the upper bound. With incomplete information, the sellers repeat the static optimum in the best equilibria for the sellers. If the virtual surplus is positive, the buyer buys every period with probability one, and he never buys otherwise. Market sharing is limited by the seller's incentives to charge the equilibrium price.