Friday Fix: Lola Lo's and Game Theory

It seems that house remixes of the pop songs of yesteryear just won’t satisfy some people. At this week’s Let’s Kill Disco – the best place to be in Cambridge on a Thursday night – some hooligans vandalised the men’s toilets; disgraceful, I know.

But fear not all you God-fearing, law abiding patrons of the three floor Tiki-themed nightclub: the manager quickly pulled the CCTV footage and obtained a grainy picture of the culprit(s). Before long, a small squad of bouncers had rounded up four suspects who resembled the despicable yob who was caught on camera. After a brief yet terse, aggressive round of questioning, one of the bouncers pointed out that their target was wearing shorts – this immediately ruled out half of the accused.

With the two falsely accused free to return upstairs and continue failing to chirpse, I was left watching a heated standoff: the manager and a handful of bouncers on one side, the two purported vandalisers (who had clearly got the wrong end of the stick since they were apologising for wearing shorts and promising it wouldn’t happen again) on the other. Being shown the footage, asked to confirm or deny whether it was really them on the security reel, both of our suspected hoodlums initially professed their innocence.

It didn’t take long for this pathetic, translucent façade to crumble, however. One of the pair accidentally snitched on themselves by identifying his own pair of trainers in the CCTV, before flipping on his friend-now-turned-mortal-rival, accusing him of masterminding the whole affair - pleading that he was nothing but a patsy, a puppet, a spineless lackey spellbound to do his bidding. After this explosive betrayal, they both owned up to their guilt.

Before I continue with this gripping tale, I would like to make a brief caveat by introducing the concept of game theory for those of you are unfamiliar. Game theory is the study of mathematical models of conflict and cooperation between intelligent rational decision-makers. It’s commonly used to evaluate psychology, economics, logic, and other areas of interest. The situation we have here is a rehashing of the famous prisoner’s dilemma.

Now, after both bathroom vandals had cracked under pressure and confessed to their heinous crimes, the blindingly obvious next step (to everyone in the lobby except them, apparently) was a (probably lifetime) ban from Lola Lo’s Cambridge. When this finally became clear, the alleged ringleader and Sir Snitchalot both tried to backtrack in a doomed attempt to save the other from punishment by claiming that they’d misspoken a mere 15 seconds earlier, and each of them claimed the incident was wholly their own fault. But alas, it was too late, and they were duly ejected from the venue.

Fig 1: a table detailing all the possible outcomes of this zero-sum game.

Using the table above, let’s explore the four possible outcomes of this scenario. For the purposes of this exercise, I’m going to refer to our two villains as Player A and Player B.

As you can see, the only scenario in which Player A escapes from this debacle unscathed is if they remain silent, with Player B taking the bullet out of the goodness of their heart. Similarly, Player B’s only way out is the same, with the roles reversed. Either of these would be what we call the socially optimal solution, the overall best-case scenario we can hope for – one person being banned but the other free to party another night.

However, if we assume that Player A and Player B are both acting in rational self-interest, it is obvious to the observer that one would not derive any benefit for themselves by confessing. This phenomenon manifested itself in how things played out in the Lola Lo’s lobby; neither was willing to save the other as it did nothing to improve their position. Consequently, they ended up with the worst possible outcome, yet the one which is logical given this set of circumstances.

We can learn valuable lessons from the chaos unleashed on the men’s bathrooms on this fateful Thursday night. Don’t vandalise the men’s bathrooms. Don’t wear shorts to a nightclub. And don’t snitch on your friend if you’re already going down in flames.