Two-Agent Collusion-Proof Mechanism Design with Both Correlations and Arbitrage

This paper studies the cost requirement for two-agent collusion-proof mechanism design. Unlike the existing results for general environments with three or more agents, it is shown that collusive behavior cannot be prevented freely in two-agent nonlinear pricing environments with correlated types. Reporting manipulation calls for distortions away from the first-best efficiency, and arbitrage calls for further distortion. Moreover, we show that the distortionary patterns are quite different for positive and negative correlations. The second-best outcome is attainable as negative correlation is vanishing, while the limit of collusion-proof efficiency is strictly lower than the second-best level as positive correlation goes to zero. Allowing arbitrage therefore breaks the continuity between correlated and uncorrelated types.