The cooperative dirty paper coding (DPC) rate region is investigated in a two-transmitter two-receiver network with full channel state information available at all terminals. The transmitters cooperate by first exchanging messages over an orthogonal cooperation channel, then they mimic a broadcast channel (BC) and jointly perform DPC to send to the two independent receivers. The allocation of network power and bandwidth between the data and the cooperation channel is studied to characterize the cooperative DPC rate region. First, the optimal sum power allocation for a multiple access channel (MAC) is presented. Then through an application of the MACBC capacity duality, the cooperative DPC rate region is evaluated under different bandwidth allocation assumptions. Cooperative DPC outperforms non-cooperative time-division (TD) only when the cooperation channel is strong, since the joint-encoding capacity gain is negated by the overhead of message exchanges in a weak cooperation channel. Moreover, the cooperative capacity advantage over TD is more pronounced at the maximum sum rate point than when the rate vector is skewed toward one of the users.