The prisoner’s dilemma is a staple of game theory. Your optimal strategy depends on your opponent’s strategy, and vice versa. If you both cooperate, you both do pretty well. If you are aggressive and your opponent tries to cooperate, you do very well. And vice versa. Finally, if you
both get aggressive, well, you both do poorly. Assuming the two players have the same interests, the “payoffs” in the four scenarios might be [1,1], [3,0], [0,3], [0,0].
There are textbooks analyzing the optimal strategy against a variety of “styles” of opponents. The start of the Singapore grand prix proved that Ferrari’s Sebastian Vettel didn’t read any of them.
Vettel qualified first, with Red Bull’s Max Verstappen in second, one car length behind him and to the left. If Vettel had called up any semi-qualified game theorist before the start, this is what he would have heard: Max is not in contention for the drivers’ championship, so he is just angling for race wins, therefore Max has little reason to be cooperative and expect aggression. Let’s dig into that conclusion.
The Singapore grand prix game theory differs from the simple example in the first paragraph because the drivers have different interests in the race.
If Verstappen and Vettel both cooperate, Verstappen is likely to stay in second place (passing is very difficult in Singapore). If Verstappen is aggressive and Vettel is cooperative, Verstappen is likely to get that race win that he’s aiming for. If they are both aggressive, maybe they crash out, but for Verstappen that’s not a whole lot worse than finishing second — as a wise man once said: “If you ain’t first, you’re last.”
So Verstappen’s payouts for the race might be [1, x] (both cooperate, Verstappen finishes second), [25, x] (Verstappen is aggressive while Vettel cooperates and Verstappen wins the race), [1, x] (Verstappen cooperates while Vettel is aggressive so Verstappen stays in second place) and [0, x] (both are aggressive and they crash out).
Now the game theorist would have explained Verstappen’s payouts and then moved on to Vettel’s own payouts. Those might be described as [25, x] (both cooperate, Vettel stays in first), [25, x] (Vettel is aggressive while Verstappen cooperates and Vettel stays in first), [18, x] (Vettel cooperates while Verstappen is aggressive, meaning that Vettel finishes second place, but still gains important ground on his primary rival Hamilton, still quite good), [-25, x] (both are aggressive, they crash out and Vettel loses 25 points to Hamilton in the drivers’ championship, a goddamn disaster).
Our game theorist would have explained that Verstappen was likely to be aggressive because of the outsized importance of a win at this point in his season. Assuming that Verstappen is aggressive, Vettel’s options are either to cooperate and get 18 points for finishing second or be aggressive and get -25 points when they crash each other out. Seems like a no-brainer. Unfortunately, Vettel seemed to have no brain. (Unlike Vettel, Verstappen had little incentive to alter his strategy based on an assumption of what Vettel would do. If he assumed Vettel was going to be aggressive, his payouts were 1 and 0.)
When the lights went out, Vettel cut across to his left to block Verstappen. It was an extremely aggressive move. Verstappen could not or did not yield to the oncoming Vettel (as predicted). Meanwhile Vettel’s teammate Kimi Raikkonen got off to a cracker of a start and was on Verstappen’s left. The three cars collided and took themselves out of the race not 10 seconds into it. (They also collected Alonso and unfortunately ended his race too, which looked very promising after his start).
Hamilton avoided the chaos by starting way back in fifth and he cruised to a win. Ricciardo came in second and Bottas third. (The race was pretty boring aside from the start, so it warrants comparatively little ink in this recap).
Even if Vettel had to pay long distance rates to reach a game theorist, it would have been worth it. He’s now looking at a very intimidating 28 point deficit to Hamilton. We will see if he can start to eat into that with only six races left.