A Matching Model for Ride-Sharing: A Non-Cooperative Game Approach Between Drivers and Riders

This study proposes an optimal matching problem between drivers and riders as a generalised Nash equilibrium problem, which finds a solution where no drivers and riders have the incentive to change their strategy. The proposed model is formulated as a (D + R) person pure strategy game, where D and R are the number of drivers and riders, respectively. We further reformulate the proposed model as a two-person pure strategy game. A solution algorithm that iteratively solves the drivers’ and riders’ sub-problem is proposed, which is proven to converge to a Nash equilibrium solution within a finite number of iterations. Finally, we numerically confirm that the proposed model yields a Nash equilibrium solution and then perform sensitivity analysis over the parameters of the proposed model.