Game Theory of Sailing: How Nash Equilibria can be applied to match racing
https://northu.com/wp-content/uploads/2020/05/MatchRacingPlaybook.pdf
Match Racing is a discipline of sailing that is full of strategy and tactics as it is two boats, racing to the finish line and ultimately trying to outsmart each other on the way. Dave Perry, who is a Five-Time Match Racing National Champion, created a play book that acts as a guide for what is the optimal move for each boat to do in a given situation. He bases these strategies off of how each boat can position themselves to have an advantage over the other according to the rules of sailing. Obviously there are many factors to consider when actually racing including boat speed, wind speed, wind shifts, length of line, time to start, etc., but for the most part these plays theoretically hold true. Assuming that wind is 7-10 knots (so no boat is too under or over powered) and the two boats are equally skilled, then Game Theory can be applied to figure out what a boat should do in the “leading” and “pushing” positions of a prestart, in order to have the best possible start. The boats attempt to maneuver themselves into optimal position by either heading high or low.
In the scenarios I have drawn, the blue boat is the “leading” boat, and the yellow boat is the “pushing” boat. The job of the leading boat is to maintain distance ahead of the pushing boat, and not allow them to get leeward (further away from the wind) to obtain overlap, thus gaining right of way on them, and to not get pushed far away from the starting line. On the flip side the job of the pushing boat, who starts off in control, is to attempt to hook the leading boat to gain control, and not overlap themselves to windward (closer to the wind) and lose control of the leading boat. I have created a table, and assigned payoff values on a scale of 0 to 10 (10 being the best possible outcome for the boat), for each given scenario. Using this table it is clear that there are Nash Equilibria (seen in drawing) that can be applied to the sport of match racing, as each boat has a best response to the other boat’s maneuver. From the chart it is obvious that yellow has more winning payoffs, then blue, but that is expected as the pushing boat is in a controlling position of the leading boat. Yellow also has a dominant strategy of going low, as no matter what choice blue makes, they will always have a higher payoff. Obviously this is a simplified version of the maneuvers that really occur during the starting process of match racing as there are other variables to consider (distance to line, time, wind, speed, etc.), but it does show that game theory is applicable. Sailors can study game theory to help minimize mistakes, and gain as many advantages as possible to help them towards winning races.