Income distribution, implementation sequence, and equity in auto ownership rationing

•Investigate the issues of income distribution, implementation sequence, and equity in the auto ownership rationing schemes.•Implementing auto ownership rationing schemes can cause inequity issues due to different changes in individual costs of different-income residents.•Pareto-improvement strategy with self-financing constraint is presented to balance the equity and efficiency.•The optimal lottery + auction (L+A) hybrid scheme outperforms the optimal auction + lottery (A+L) hybrid scheme in terms of expected social surplus.•The optimal A+L Pareto-improvement strategy is better than the optimal L+A Pareto-improvement strategy in terms of expected social surplus.•Residents’ income distribution has no significant effects on the properties of the models.