Urban rail transit systems in many cities are experiencing crowding during peak periods due to rapid population growth. Incentive-based demand management strategies aim to better utilize the available capacity by shifting peak travel to off-peak periods. Various deployments have demonstrated the crowding-reduction potential of incentives in reducing crowding but they have also shown that such strategies are inefficient with many passengers receiving the incentives but relatively few contributing to crowding reduction. This paper proposes a reverse auction-based, individualized incentive strategy to encourage individual passengers to switch travel from peak to off-peak periods. The proposed approach is individualized, participatory, and explicitly accounts for individual characteristics and the potential contribution of their behavior changes to the system. Extensive experiments are conducted to demonstrate the approach using AFC data from Hong Kong's urban rail network. The results indicate that auction-based individualized incentives can enhance the system efficiency by strategically selecting passengers as winners whose behavioral changes contribute to the system performance. It also highlights the importance of correcting the information bias of perceived travel behavior between bidders and the population when operators select bid winners.