Nonlinear Pricing with Arbitrage: On the Role of Correlation

In nonlinear pricing environment with correlated types, we characterize optimal selling mechanisms when buyers could form a coalition to coordinate their reports and to arbitrage on the goods. We find that when the types of agents are weakly positively correlated, the optimal weakly collusion-proof mechanism calls for distortions away from e±ciency obtained without arbitrage; when the types are weakly negatively correlated, the monopolist can achieve the same profit regardless of whether or not buyers can arbitrage on their goods. Allowing arbitrage within coalitions result in right discontinuity between the correlated and uncorrelated environment, but the left continuity is still available.