As higher buildings are constructed, more efficient elevator systems are needed. In order to increase the transportation capacity within buildings, the addition of elevators has been a commonly used strategy. However, due to the space occupied by each elevator the number of them that can be added becomes limited. To solve this problem multicar elevator (MCE) systems, consisting of several elevator cars (cages) operating independently within the same shaft (vertical passageway), have been proposed. Nevertheless, due to the need to avoid interference between cars, conventional elevator group control methods cannot be applied in MCEs. Therefore, an MCE group control method capable of offering an optimal performance while efficiently preventing car interference is required. In our research we propose an average reward learning method in which car agents develop a call response policy that can reduce the service completion time and the occurrence of interference events. Simulation results show our method has good performance in the interfloor traffic pattern.