Balancing Efficiency and Equality in Vehicle Licenses Allocation

Due to traffic and air quality concerns in urban cities, many big cities have begun to adopt the vehicle licenses quantitative control policies. In these cities, a limited number of vehicle licenses are allocated among a very large number of potential car buyers every one or two months. The current allocation mechanisms differ from city to city. Several mechanisms have been developed and implemented in reality, such as auction, lottery, lottery with reserved price, and the simultaneous auction and lottery. In this work, we target to design the optimal mechanism to balance efficiency and equality in practice. We first propose a unified two-group mechanism framework that either includes or outperforms all the existing mechanisms. Besides, the unified framework also leads to easy implementation in reality due to its truthfulness and simple structure. Under this framework, assuming the players' private values are drawn independently from a common distribution, we prove the optimal mechanism is always sequential auction and lottery. Besides, the optimal allocation rule depends only on the total number of players and the total number of licenses for all commonly used distributions. We then extend the two-group framework to a general multi-group framework. The experimental results show us the optimal two-group mechanism is the best choice in practice. Thus, our work provides an effective tool for social planner to design truthful mechanisms to maximize the social efficiency under any equality level. We also discuss possible applications of our result to resource allocation in other settings