A Stackelberg Game Approach for Three-Player Autonomous Racing

Abstract

This paper considers the autonomous racing of three cars, including a team of two cars and an opponent car. The competition is modeled as a two-leader one-follower Stackelberg game which can be called the sequential game. Leaders select the trajectories which make the max payoffs of the team and the follower does its best response to the actions of the team. Given that the Stackelberg equilibrium is not unique in both games, rather than selecting one strategy stochastically, the cost functions are designed for the players to cope with multiple strategies that have the same progress. The competitions are performed in a receding horizon fashion, and the aim of the research is to study the effects of cooperation and make the team win the competition under collision and road constraints.