Equilibrium modeling of mixed autonomy traffic flow based on game theory

While much attention was paid to the interactions of human-driven and automated vehicles at the microscopic level in recent years, the understanding of the macroscopic properties of mixed autonomy traffic flow still remains limited. In this paper, we present an equilibrium model of traffic flow with mixed autonomy based on the theory of two-player games. We consider self-interested traffic agents (i.e. human-driven and automated vehicles) endowed with different speed functions and interacting with each other simultaneously in both longitudinal and lateral dimensions. We propose a two-player game model to encapsulate their interactions and characterize the equilibria the agents may reach. We show that the model admits two types of Nash equilibria, one of which is always Pareto efficient. Based on this equilibrium structure, we propose a speed policy that guarantees the realized equilibria are Pareto efficient in all traffic regimes. We present two examples to illustrate the applications of this model. In one example, we construct flux functions for mixed autonomy traffic based on behavior characteristics of agents. In the other example, we consider a lane policy and show that mixed autonomy traffic may exhibit counterintuitive behaviors even though all the agents are rational. • Propose a new game theoretic approach to model the equilibria of mixed autonomy traffic. • Prove that agents in mixed autonomy traffic can reach two types of Nash equilibria. • Prove that there always exists at least one Pareto efficient Nash equilibrium in all traffic regimes. • Describe a speed policy that guarantees attaining Pareto efficient equilibria. • Illustrate a counterintuitive behavior of mixed autonomy traffic when a lane policy is introduced.