741. Optimizing Pit Stop Strategies with Competition in a Zero-Sum Feedback Stackelberg Game
Invited abstract in session HD-22: Applications of Game Theory in Operations Management , cluster Game Theory and Operations Management.
Thursday, 14:15-15:45Room: FENH202
Authors (first author is the speaker)
| 1. | Charles Thraves
|
| Universidad de Chile |
Abstract
The current work presents an application of a zero-sum feedback Stackelberg game for optimizing pit stop strategies in Formula 1. The result of a race not only depends on a driver’s performance, but also on pit stop decisions - necessary (among other things) to change used tires for new ones. Indeed, tires degrade with their usage as more laps are raced, and, therefore, lap times are affected. During a race in Formula 1, there are three tire compounds: soft, medium, and hard. Softer tires allow faster lap times, but do not last as many laps as the harder compound, because the former degrades faster than the latter.
An additional complexity of the problem we consider is the competition between drivers (such as overtaking) during a race, affecting their lap times; thus, drivers’ decisions could account for their opponents’ decisions. Most works in this area have addressed the problem as an optimization problem, either neglecting competition or accounting for it in simulations or past decisions, but not in a game theory sense.
We present a model where two drivers compete against each other during a race; 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, the problem is formulated as a zero-sum feedback Stackelberg game, where, in each lap, the driver leading the race decides first, followed by the decision of the driver who is second. The game is solved via Dynamic Programming. In addition, at the beginning of the race, both players solve a simultaneous game to decide the tire compound to start the race. The formulation introduced also allows for the inclusion of random events, such as yellow flags (when cars must slow their speed due to a race incident).
We show the existence of game equilibrium and provide an algorithm to find this; then, we solve instances of the problem, based on a real race. We perform numerical experiments comparing the performance of a miopic driver (who does not account for his opponents’ decisions) versus a strategic one and show omitting the strategic behaviour of the opponent car leads to worse race results in almost all scenarios.
Keywords
- Game Theory
- Programming, Dynamic
- Applications, Sports
Status: accepted
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