Optimizing pit stop strategies in Formula 1 with dynamic programming and game theory

Optimization of pit stop strategies in motorsports is not trivial. Most existing studies neglect competition, or account for it using simulation or historical data, but not in a game theory sense. In this work, we present a model, based on Formula 1, in which two drivers optimize their pit stop strategies. Each car decides at each lap whether to continue on-track, or to take a pit stop to change tires to one of the three tire compounds available. Since the drivers' decisions affect each other due to interactions such as overtaking, the problem is formulated as a zero-sum feedback Stackelberg game using Dynamic Programming, in which in each lap the race leader (follower) decides first (second). In addition, drivers decide simultaneously their starting tire compounds. The formulation allows for the inclusion of uncertain events, such as yellow flags, or randomness in lap times. We show the existence of the game equilibrium, and provide an algorithm to find it. Then, we solve numerical instances of the problem with hundreds of millions of states. We observe how drivers' different objective functions induce different race strategies. In particular, if players maximize the probability of winning, instead of the time-gap with their opponent, their actions tend to be more risk taking. Our instances show that a strategic driver who faces another who ignores competition, increases the winning odds by more than 15% compared to when both race strategically. Finally, yellow flags tend to increase the winning chances of the driver with the worst performance.