Periodic beacons in vehicular ad hoc networks are transmitted with high message frequency to achieve the higher level of awareness required for the vehicular safety applications. Currently, the existing 10-MHz control channel in the dedicated short range communication (DSRC) standard is not compliant with the communication requirements in vehicular safety applications, i.e., the stipulated amendments in the DSRC offer little relief to congestion caused by the periodic beacon transmissions on the control channel, which adversely affects the message reception. In this paper, we seek to address the problem of congestion with a transmit power adaptation approach, based on the principles of cooperative game theory. The proposed approach, Adaptive transmit power Cooperative Congestion Control (AC3), is designed to allow vehicles to select their transmit power autonomously with respect to their local channel congestion. Since the number of neighbours of each vehicle and their corresponding transmit power levels vary, AC3 requires that each vehicle reduces its transmit power fairly during congestion. Explicitly, the proposed approach introduces the notion of marginal contributions of vehicles towards congestion and determines a fair power decrease for vehicles using a shapely value system model. This model requires the vehicles with the highest marginal contributions to reduce the most transmit power and vice versa. The simulation results demonstrate the utility of the proposed approach (i.e., capability to determine fair power decrease for an effective congestion control).