Optimal collusion with private information

Me analyze collusion in an infinitely repeated Bertrand game, where prices are publicly observed and each firm receives a privately observed, i.i.d. c ost shock in each period. Productive efficiency is possible only if high-co st firms relinquish market share. In the most profitable collusive schemes, firms implement productive efficiency, and high-cost firms are favored wit h higher expected market share in future periods. If types are discrete, th ere exists a discount factor strictly less than one above which first-best profits can be attained using history-dependent reallocation of market shar e between equally efficient firms. We also analyze the role of communicatio n and side-payments.