Two-agent collusion-proof implementation with correlation and arbitrage

This paper characterizes the optimal collusion-proof mechanism in a two-agent nonlinear pricing environment. Our model allows agents to have correlated types and to reallocate their total purchases among themselves. We show that, under strongly negative correlation, the coalition will, sometimes, be torn apart at no cost. Under positive or weakly negative correlations, however, the threat of collusion forces the principal to distort allocation away from the first-best level obtained without collusion. We also show that, in contrast to the result of Laffont and Martimort (Econometrica 68:309–342, 2000), when the correlation is almost perfectly positive, the possibility of arbitrage prevents the principal from approaching the first-best efficiency.