An Open-loop Stackelberg Game Approach to the Dynamic Congestion Pricing Problem

Abstract

This paper considers the problem of dynamic congestion pricing which determines an optimal toll schedule to be charged at the entrance of a bottleneck on a single-destination traffic network. A two-person nonzero-sum Stackelberg differential game model is formulated when the underlying information structure is open loop. Characteristics of the Stackelberg equilibrium solution are analyzed. The Pontryagin minimum principle is applied to derive the necessary conditions from which the open-loop Stackelberg equilibrium strategy can be obtained. The heuristic algorithm which obviates an evaluation of the gradient vector of the Hamiltonian is also proposed.