The current market design of mandatory vehicle insurance in Brazil has raised questions regarding its model highlighting inefficiency in the transfer of resources from vehicle owners to victims of traffic accidents and lack of incentive for efficiency in resource management. This is a highly complex mechanism with a hybrid nature (public policies and private insurance) whose design is a constant challenge for the Brazilian regulator. Looking to mitigate some of the problems, we provide an option to the current model in which the government directly defines the insurance company and the premium. This study proposes a new market design, using auctions for a more transparent and efficient process for allocation and price discovery for DPVAT Insurance. In a uniform reverse multi-unit auction, insurers bid quantities and premium by vehicle category and State. The results indicate that structure of the insurance industry and government decisions play a key role in market performance.