text: In this study, we formulate positive and negative externalities caused by changes in the supply of shared vehicles as ride sharing games. The study aims to understand the price of anarchy (PoA) and its improvement via a coordination technique in ride sharing games. A critical question is whether ride sharing games exhibit a pure Nash equilibrium (pNE) since the PoA bound assumes it. Our result shows a sufficient condition for a ride sharing game to have a finite improvement property and a pNE similar to potential games. This is the first step to analyze PoA bound and its improvement by coordination in ride sharing games. We also show an example of coordinating players in ride sharing games using signaling and evaluate the improvement in the PoA.
  @cite_14: Dynamic ride-share systems aim to bring together travelers with similar itineraries and time schedules on short-notice. These systems may provide significant societ al and environmental benefits by reducing the number of cars used for personal travel and improving the utilization of available seat capacity. Effective and efficient optimization technology that matches drivers and riders in real-time is one of the necessary components for a successful dynamic ride-share system. We systematically outline the optimization challenges that arise when developing technology to support ride-sharing and survey the related operations research models in the academic literature. We hope that this paper will encourage more research by the transportation science and logistics community in this exciting, emerging area of public transportation.
summary: According to a review of sharing studies in transportation areas @cite_14 , there are few game theory studies on externalities and coordination of players' moves in vehicle sharing problems. Traditional studies on sharing include the optimization of vehicle routes for picking up all passengers (the Dial-a-ride problem ), problems of splitting passengers' fares according to their riding distances, optimization of locations of carpool stations, and problems of relocation of carpool vehicles among stations. Those studies mainly focus on optimization problems under given moves (origins and destinations) of passengers and fixed drivers of vehicles, and therefore, do not analyze the PoA when passengers strategically choose their moves in response to the moves of other passengers and vehicles. The review states that there are no studies on coordination of players' moves to improve the efficiency of sharing or reduce the PoA.