Game Theory Applied

A friend of mine recently posted the the following conundrum to his blog:

I found the deck of cards from a board game called scrupples (it poses you a dilemma and your opponents guess how you would respond) and I thought up another one completely off the top of my head:

"You and two other people are temp workers in a large corporation hired for one month to do some simple, repetitive data entry. One of your co-workers over-hears the boss say that the temps are very good and that they are going through the work so quickly they’ll probably let one of them go. Your co-worker suggests to you that all three of you go slow from now on. What do you do?"

I found the application of game theory to this question more interesting than the ethical implications it posed, so I wrote a long comment in reply to it. Then, realising that the comment was so long that it probably deserved it’s own blog post, I wrote this.

I recommend that you come up with your own answer to Matt’s question before you read my post.

Ah yeah; I’ve played that game. It’s far more fun when you start making up your own.

Now, on to your question – it’s more complex that it immediately appears – at first it’s a simple question of ethics: go slower to keep your job or keep doing a good job for a one-in-three chance of losing it. Based on that, even, it’s not so simple a question, and my answer would depend on how much I wanted to keep the job, which depends on factors like how much I needed the money, etc.

But it’s not that simple; thanks to a little application of game theory, because it turns out that if you do make the decision to slow down, but your two co-workers, faced with the same decision, speed up, then it’s probably going to be you that they let go, on account of you being the least productive of the three. Assuming that all three temps are equally capable of thinking through this logic and do not communicate with each other any further, I would anticipate that all three would work even harder in an effort to impress. After all, if you’re the one who’s deliberately slow, you have a 1-in-3 chance of being fired, but if you’re deliberately fast, you have a 1-in-3 at worst (in the situation that everybody goes fast, assuming that all three are equally competent workers).

Of course, this is a somewhat sterile view of the world: in the end, there are other major factors that can’t be accounted for in simple probabilistic terms: it’s unlikely that all three temps are equally proficient, or that they all want the job badly enough to put in the same level of extra effort, or that they don’t trust each other enough to form a meaningful "slow conspiracy." There’s lots of factors that game theory doesn’t take into account here: but nonetheless, it seems to work: I’ll pick a related example.

There is a party game I’ve taken part in a few times in which a team of individuals is charged with the task of slowly lowering a long thin pole to the ground without any individual member losing contact with it. The players are stood in a staggered pair of lines, facing one another, with the stick held between them at about nipple-height. Each player supports the stick with exactly one finger. Then, as a team, they have to lower the stick to the ground, without anybody losing contact with the stick. This makes a conflict of rules:

1. each individual wants to be touching the stick (from underneath), but
2. the team wants the stick to go down.

What happens? The stick moves up. The effect is magical to watch, because if you’ve got over about six people none of them "feels" like they’re part of the "moving up" process, but it’s still happening. Everybody blames everybody else. In actual fact, each person is re-asserting their position against the stick (by moving their finger up in response to it moving away from them) so as to meet rule 1. And all it takes is a little involuntary vibration (easy done, when you’re supporting part of a long stick on one finger) to kick the process off. It’s a good team-building activity, and it’s great to spectate, too.

Transplanted to your hypothetical (?) situation, the height of the stick represents the speed of work of the fastest worked. Game theory predicts that you will all want the best for yourself, ultimately, and so the rules are as follows:

1. each individual wants to be touching the stick (i.e. wants to be the fastest worker), but
2. the team wants to the stick to go down (i.e. work speed in general becomes slower).

Therein lies the basis of my prediction. What do you think?