Friday, February 18, 2011

Teamwork and Drafting

This morning I saw an interesting story on a strategy in car racing: two-car teamwork by drafting (and trading off who goes first). Although the strategic two-car drafting is new, drafting from other cars is not new in professional car (or bike) racing.
Like the old adage "it takes two to tango," drafting can only be accomplished with two or more cars. When the lead car rockets down the track it pushes through the air leaving a disturbed, or "dirty," wake behind it. The second car can slip into that disturbed air stream and reap the benefits -- that is, if the driver is talented.

At superspeedways like Alabama's Talladega and Florida's Daytona International, where speed is limited by a restrictor plate rule, long lines of drafting cars take advantage of the car in front to allow greater speeds and better fuel efficiency.

These advantages create a strong motive toward cooperation within a pair, but what happens at the end of the race?

Let's say that a drafting pair is comprised of Bob and Steve. Conditional on making it to the final lap with enough gas to make a final push, assume that you would rather be in front than behind because you can obstruct the other driver. We can represent this choice at the final node in a game tree. At the conclusion of the second-to-last lap, suppose it is Steve's turn to give the lead back to Bob.

Let's translate this into some game theory. Here's what Steve's choice looks like in the final subgame of the race. Steve chooses which path to follow and he gets the payoff from the first number in the ordered pair.

The way I set the payoffs up, Steve likes saying in front better than giving the lead back to Bob. So, that's what he'll choose. As long as he prefers winning the race (and it is an advantage to lead the race going into the final lap), Steve won't want to give the lead back to Bob at the second-to-last lap.

Knowing this, Bob won't want to give his lead back to Steve at the third-to-last lap. Take this argument back 499 laps and you can see that this two-car pairing is a tenuous agreement. These tenuous agreements may form to the betterment of the pair in competition with other pairs, but the possibility that the agreement breaks down creates some interesting tension (I never thought I'd say that about car racing).

Yes, there are gains from trading who drafts, but if I am Steve, it would be even better for me if Bob just cut the wind for me and I didn't have to cut the wind for him. As long as Bob wants to win the race, Steve will have a hard time convincing Bob to go first.

What if Bob and Steve were on the same "team" with a shared objective that the team wins the race? As long as a win for the team is a win for both, Bob would be willing to cut the wind. But, the two-car partnership is still doomed because Bob will run out of gas sooner than Steve. Steve will have to go at least one lap without Bob's drafting services, and finding Bob's car again among the sea of competitors may be a tough task.

Maybe there's a way to add more cars to the team so Steve with a drafting buddy who will his wind (and save his gas). Switching front cars at full speed without disrupting Steve's racing sounds like a tough deal to me. I'll leave that to the professionals while I stick to the speed limit.

2 comments:

  1. Tony, I think you'll get a kick out of this video (if you haven't already seen it!)

    http://www.youtube.com/watch?v=BkkTSVVrPYk

    ReplyDelete
  2. Also:

    http://en.wikipedia.org/wiki/Sprint_(cycling)

    ReplyDelete

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