The Tit-For-Tat Conjecture

Suppose you and I are going to play a co-operation game. There are many strategies for these, but the most beneficial is tit-for-tat: start by co-operating, then repeat the previous move of the other player. It’s simple, but it doesn’t dominate all the others. But it does give the maximum reward. If I know you’re going to use it, I may as well climb on board for those maximum rewards as well. Tit-For-Tat is a fairly rare strategy: it works even when the other person knows you’re using it. In fact, it works especially when the other person knows you’re using it.

One that fails if it’s public knowledge is the Secretary Strategy. In this, an employer is hiring, and has a limited time to pick a new person. It turns out that the most effective strategy is for them to look at the first third of the candidates, and then hire the first candidate better than all the ones they have already seen. This will get them the best candidate in 37% of hires. Some, of course, will never hire anyone, because the best was in the first third. It’s not a reliable strategy.

In this economy, recruitment is done through agencies, and they get to know the habits of the recruiter. If the agency know the employer uses the Secretary Strategy, they will arrange for the employer to see lesser-quality applicants at first, so they can place a reasonable one rapidly. The Secretary Strategy fails because the employment agent invalidates one of the assumptions, which is that candidates arrive at random. But then that’s the point of strategies and gaming. The only way out for an employer is to recruit directly, like they used to. Even then, in a small world, which some industries are, an interviewee finding she is the first might politely decline, on the grounds that ‘everyone knows you never hire the first person you see’. This denies the employer the opportunity to calibrate that the Strategy provides. The only way out of that is to lie to the candidates about their place in the queue: that’s not such a smart idea.

Most strategies are like this: they work as long as the other side don’t know. What makes Tit-For-Tat different? The Secretary Strategy predicts the future behaviour of its user, which allows others to game it. Tit-For-Tat can also be predicted, but the prediction is based on the other person’s behaviour, not its user’s intentions.

Strategies are, amongst other things, formalised intentions. If we know the strategy, we have a good idea about the objectives it is intended to achieve, and if we know that, we can make more informed guesses about the other ploys the other side might use.

Here’s a Conjecture: any strategy that works even when the other side knows you’re using it is equivalent to Tit-for-Tat.

If this is true, the immediate consequence is: unless you’re using Tit-for-Tat, your strategy can be gamed to your disadvantage.