Optimizing Pit Stops Strategies with Competition in a Zero-Sum Feedback Stackelberg Game in Formula 1
40 Pages Posted: 6 Jun 2023 Last revised: 12 Sep 2023
Date Written: September 11, 2023
Optimization of pit stop strategies motorsports is not trivial. Most existing works neglect competition, or account for this 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 strategy. Each car decides on each lap whether to continue on-track or to do 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, where 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 define and show the existence of the game equilibrium and provide an algorithm to find this. Then, we solve numerical instances of the problem with hundred of thousands of states. We observe how drivers' different objective functions induce different race strategies. In particular, when players' maximize the probability of winning instead of the time-gap to their opponent, their actions tend to be more risk seeking. Our instances show that a strategic driver facing a myopic one increase the winning odds by more that 15% compared to the case when both are strategic. Finally, yellow flags tend to increase the chances of winning of the driver with worst performance.
Keywords: Feedback Stackelberg, Zero-Sum Game, Dynamic Programming, Formula 1, Pit Stop Strategy
JEL Classification: C44, C73, C61
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