Routing strategies under the aegis of dynamic traffic assignment have been proposed in the literature to optimize system performance. However, challenges have persisted in their deployment ability and effectiveness due to inherent strong assumptions on traveler behavior and availability of network-level real-time traffic information, and the high computational burden associated with computing network-wide flows in real-time. This study proposes an incentive-based decentralized routing strategy to nudge the network performance closer to the system optimum for the context where all vehicles are connected and autonomous vehicles (CAVs). The strategy consists of three stages. The first stage incorporates a decentralized local route switching dynamical system to approximate the system optimal route flow in a local area based on vehicles' knowledge of local traffic information. The second stage optimizes the route for each CAV by considering individual heterogeneity in traveler preferences (e.g., the value of time) to maximize the utilities of all travelers in the local area. Constraints are also incorporated to ensure that these routes can achieve the approximated local system optimal flow of the first stage. The third stage leverages an expected envy-free incentive mechanism to ensure that travelers in the local area can accept the optimal routes determined in the second stage. The study analytically discusses the convergence of the local route switching dynamical system. We also show that the proposed incentive mechanism is expected individual rational and budget-balanced, which ensures that travelers are willing to participate and guarantee the balance between payments and compensations, respectively. Further, the conditions for the expected incentive compatibility of the incentive mechanism are analyzed and proved, ensuring behavioral honesty in disclosing information.