Inducing Desired Equilibrium in Taxi Repositioning Problem with Adaptive Incentive Design

We study the problem of designing incentives to induce desired equilibrium in taxi repositioning problems. In this scenario, self-interested idle drivers will update their repositioning strategies with observed payoff. Meanwhile, the platform will adaptively design incentives to induce a better Nash equilibrium for global efficiency. We formulate the problem as a bi-level optimization problem where the incentive designer and idle drivers simultaneously update their decision variables. We prove that drivers' strategies will reach Nash equilibrium, and the incentive designer's objective function will reach optimality under Polyak Lojasiewicz (PL) condition. Furthermore, we derive a sufficient condition for the PL condition to hold for the upper-level objective function and lower-level agents' payoff function. Finally, we demonstrate the efficiency of the proposed method by numerical results.