In this paper, we evaluate a lottery-based revenue-neutral incentive mechanism to reduce the congestion in urban transportation systems. Specifically, we test the use of random lottery-based reward schemes to promote public transit usage during offpeak periods. We derive the theoretical equilibrium for this decision-making game and test the validity of the proposed mechanism through monetized laboratory experiments. We use methods from experimental economics to investigate the behavioral assumptions within such an incentive-based mechanism. We find counterintuitive results where a Pure Nash Equilibrium explains behavior in one regime and Quantal Response Equilibrium explains behavior in another regime. Specifically, there is no shift to off-peak periods when the expected value of traveling in the off-peak is less than that at peak, which is explained by a Pure Nash Equilibrium. However, there is a substantial shift to the off-peak period when the expected value of traveling in the off-peak is larger than that of the peak, but much less than that predicted by a Pure Nash Equilibrium. The Quantal Response Equilibrium performs reasonably well in this condition, and we conclude that risk attitudes play a significant role in explaining behavior in lottery-based incentive mechanisms. This study, which relies on the gamification of travel behavior, finds that the proposed mechanism can provide a sustainable shift in users' choices.