Relationships and Dominant Strategies…

Well, yes, I know what your first thoughts are. There is no way we can explain relationships with economic science. But let me tell you what I think. As in my first post, everybody acts on a rational way, seeing his own set of information, and having their own incentives to achieve a better utility… And so do men and women in relationships.

So, first of all, I want to introduce you the prisoners’ dilemma. This is a classic game theory example, in which we can see that, sometimes, when one’s outcomes are also determined by other individuals, our strategy as individuals won’t necessarily be the ones that will lead us to the highest outcome or utility.

Consider the following situation (Source: Wikipedia):

“Two suspects are arrested by the police. The police have insufficient evidence for a conviction, and, having separated both prisoners, visit each of them to offer the same deal. If one testifies ("defects") for the prosecution against the other and the other remains silent, the betrayer goes free and the silent accomplice receives the full 10-year sentence. If both remain silent, both prisoners are sentenced to only six months in jail for a minor charge. If each betrays the other, each receives a five-year sentence. Each prisoner must choose to betray the other or to remain silent. Each one is assured that the other would not know about the betrayal before the end of the investigation. How should the prisoners act?”

What do you think? The most ‘rational’ thing to do is that both of them remain silent, and they will serve 6 months each, and we are done. However, if prisoner A stays silent, then prisoner B can testify, and he will go free, while A will be sentenced to 10 years in jail. So A cannot take that risk, he will prefer to betray B, even though he will be better off if both A and B remain silent. So the dominant strategy will be ‘mutual betrayal’, and each of them receiving a five-years sentence, which is clearly not the best outcome they could have achieved if they would have agreed beforehand.

This is similar to women and men behaviors in relationships. When a man starts dating a woman, and they happen to like each other, they will probably want, at least at the beginning, to talk over the phone all the time, or see each other all the time. In many cases this indeed happens, and they are a happy couple – the happiest they can be.

However, this is probably not the common case. Why? Well, if the girl starts calling the guy too much, or vice-versa, then they will be giving a signal to the other that they are “easy to catch”. But usually, in relationships you don’t want this to happen. Girls want to be seduced, and see the man working hard to achieve that. Similarly, men don’t want girls to think that they are too crazy about her or that they don’t have other girls that they can invite as well. Both men and women choose a strategy, the "hard to get" strategy, in which they don’t pay too much attention to the other one…

So what does this have to do with game theory? Well, this is a game. Both the man and the woman will be better-off by avoiding all these “hard to get” games. They will be able to save some time, and avoid uncomfortable situations. But in any case, the equilibrium is to play it the hard way.

Why? Imagine player one stops playing the “hard to get” strategy – and say starts calling more or caring more than usual for the other. Then player two can play two strategies. He/She can respond in the same way, and if they both keep playing that strategy without deviating, they might reach a better outcome. However, if player two decides to play back the “cooperative” strategy, but player one in response starts playing the “hard to get” strategy, then player two will look like an idiot… Player two will be calling and inviting player one, while player one will be indifferent and rejecting some of the invitations at a certain rate. Player two will feel bad about it, and will understand that player one is playing “hard to get”. What is the only response to that? Choosing as your optimal strategy the “hard to get” one.

We finally reach an equilibrium in which men and women choose to play a “hard-to-get” strategy being this one the dominant strategy. And sometimes, even though this can have a positive outcome, it won’t be as high as the other equilibrium (both playing the “cooperative” strategy)… at least in terms of time and avoiding uncomfortable moments.

So, you see... people are rational...