This paper proposes a method for adaptively assigning service areas to self-driving taxi agents in ride-share services by using a centralized deep Q-network (DQN) and demand prediction data. A number of (taxi) companies have participated in ride-share services with the increase of passengers due to the mutual benefits for taxi companies and customers. However, an excessive number of participants has often resulted in many empty taxis in a city, leading to traffic jams and energy waste problems. Therefore, an effective strategy to appropriately decide the service areas where agents, which are self-driving programs, have to wait for passengers is crucial for easing such problems and achieving the quality service. Thus, we propose a service area adaptation method for ride share (SAAMS) to allocate service areas to agents for this purpose. We experimentally show that the SAAMS manager can effectively control the agents by allocating their service areas to cover passengers using demand prediction data with some errors. We also evaluated the SAAMS by comparing its performance with those of the conventional methods.