Liability Design for Autonomous Vehicles and Human-Driven Vehicles: A Hierarchical Game-Theoretic Approach

Autonomous vehicles (AVs) are inevitably entering our lives with potential benefits for improved traffic safety, mobility, and accessibility. However, AVs' benefits also introduce a serious potential challenge, in the form of complex interactions with human-driven vehicles (HVs). The emergence of AVs introduces uncertainty in the behavior of human actors and in the impact of the AV manufacturer on autonomous driving design. This paper thus aims to investigate how AVs affect road safety and to design socially optimal liability rules for AVs and human drivers. A unified game is developed, including a Nash game between human drivers, a Stackelberg game between the AV manufacturer and HVs, and a Stackelberg game between the law maker and other users. We also establish the existence and uniqueness of the equilibrium of the game. The game is then simulated with numerical examples to investigate the emergence of human drivers' moral hazard, the AV manufacturer's role in traffic safety, and the law maker's role in liability design. Our findings demonstrate that human drivers could develop moral hazard if they perceive their road environment has become safer and an optimal liability rule design is crucial to improve social welfare with advanced transportation technologies. More generally, the game-theoretic model developed in this paper provides an analytical tool to assist policy-makers in AV policymaking and hopefully mitigate uncertainty in the existing regulation landscape about AV technologies.