Game theory, the Prisoner’s Dilemma and romantic relationships

I have been reading a book on game theory and have been cogitating on how it applies to romantic relationships. The book in question is Game Theory at Work by James Miller. In the book, various types of game are described (these being games played in every day life rather than artificial things with boards or cards), one of the most interesting being the Prisoner’s Dilemma. In order to save myself the bother of describing to you how this works, I’m just going to quote the explanation from the 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 from the other) for the prosecution against the other and the other remains silent (cooperates with the other), 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? 

This conundrum can be represented graphically thus:

	Prisoner B Stays Silent	Prisoner B Betrays
Prisoner A Stays Silent	Each serves 6 months	Prisoner A: 10 years Prisoner B: goes free
Prisoner A Betrays	Prisoner A: goes free Prisoner B: 10 years	Each serves 5 years

 

As you look at this, it is obvious that the best course of action is for the prisoners to cooperate so that they each get 6 months. But if you are only concerned about yourself, you are better off betraying in the hope that you will get off free and this course of action will make sure that whatever happens you will never serve 10 years. As both prisoners take the same rational decision, both end up serving 5 years – not a great outcome.

 

You can see an analogous situation with nuclear disarmament. In this case, the situation looks like this:

	Country B Disarms	Country B maintains nuclear weapons
Country A Disarms	End of possible nuclear nightmare	Country A: weak Country B: all powerful
Country A maintains nuclear weapons	Country A: all powerful Country B: weak	MAD – possibility of armageddon & end of world

No country will risk being at the mercy of another, so it maintains nuclear weapons. It would be better to renege on a possible arms limitation treaty to ensure dominance as otherwise, another country might do it and you would be stuffed. Thus we have nuclear weapons.

 

Fair enough. That was all for illustration purposes. What, you ask, has this got to do with romantic relationships? Well, consider the following matrix:

	Boy loving	Boy mean
Girl loving	Romantic bliss	Girl: devastated Boy: feels admired and confident
Girl mean	Girl: feels admired and confident Boy: devastated	Break up - unhappiness

 

In romantic relationships, it is essential for both parties to trust each other and expose their vulnerability if they are going to get to romantic bliss. But this is a highly risky strategy. If you show your vulnerability and your significant other doesn’t, then you risk getting very hurt. Your best bet is to hold back on exposing your vulnerability, keep up some sort of guard and continue to be mean. In this way, nothing too awful can happen to you. It looks like what game theorists call a “dominant strategy”, the best outcome for you no matter what the other person does. You won’t get to romantic bliss, but you won’t get devastated either. Not falling in love, therefore, looks pretty wise, which somehow seems counter-intuitive (like all the best Prisoner’s Dilemmas).

Now let’s take this a stage further. Suppose you are a very good-looking girl and have to beat off suitors with a stick. It is likely that you will be even meaner than the average girl. (The same goes for boys of course, but as we will see, the girl case is easier to comprehend). Why is this so?

As a good-looking girl with many admirers, your job is to end up with the best suitor you can, in other words to sort the wheat from the chaff. Getting a partner isn’t a problem; getting the right one is. Playing the mean strategy benefits you in many ways. Firstly, it eliminates all but the most committed – the others will simply give up if you keep rebuffing them and making them feel inadequate.

Secondly, it increases your perceived value. As we all know, anything you can get without effort or expense is barely worth having. The more you play hard to get, the greater the prize that your suitors perceive. This is behind the wisdom of never sleeping with anyone on a first date. If you cave in that quickly, a lot of your mystery and perceived value evaporates and you risk being dumped. With greater value, you can aspire to better presents, more flowers, better meals and nicer weekends away.

Thirdly, as we have seen above, it’s a non-losing strategy. So long as you are mean and non-committal, you have no risk of getting hurt. Your strategy should thus be to increase your desirability with clothes, grooming and whatever accoutrements you can muster, and decrease your availability (“Sorry, I have to stay in to wash my hair”).

This is, of course, the stuff of myth and fairy tale, wherein the Prince or suitor has to slay dragons, cut through thorns and perform countless other disagreeable tasks in order to win the Princess, whose only real obligation is to be beautiful.

If you are not such a good-looking girl, it’s a riskier strategy in that you might have a lot fewer suitors and they might not be prepared to go to all that trouble. Similarly, if you are a guy, you are at an initial disadvantage in that you are the one, in western society, who is supposed to be making the running, ie, increasing your vulnerability and risk of rejection by asking in the first place. Nothing stops you, after hooking your girl, of course, to start to play the mean strategy, but it can’t be your first move.

Back to our princess. Having discovered that playing hard to get is a winning strategy, you are faced with a problem. You can’t actually get to romantic bliss by continually playing this strategy – and that is your ultimate aim. To get there, you have to eventually decide to be nice. When should you do this? Clearly, when the suitor meets expectations. But this is very similar to the person holding shares which have appreciated in value. When do you cash in and sell? Might they not be worth more tomorrow? Suppose they go up 30% after you sell them – what do you feel like then?

So you’ve found a good suitor who has met the criteria, but might you not meet a better one in the near future? After all, no one is perfect, you hold all the cards, so why not wait for the real Prince Charming? He’s got to be out there somewhere. If you live in an urban environment, where you come into contact with many people and a lot of potential suitors, you’d be more likely to hold out for the jackpot. Also, playing the mean strategy might become a force of habit. As we have seen, it works very well – up to a point - so you might develop behaviours – high maintenance behaviours, if you like – which become second nature. As you put off showing your vulnerability, your armour might become like a second skin which you find very difficult to slough off at the opportune moment.

All the above refers to a well-adjusted individual. But let’s suppose, for the sake of argument, that you aren’t that well-adjusted. Seems reasonable. After all, who is? Maybe, as a budding princess, you learned early in life that you only had to stamp your foot a bit and you got what you wanted. The mating game would only reinforce this conviction. You might get to the stage when what you most desire is romantic bliss, but you just can’t bring yourself to adopt the nice strategy as you never have for any length of time. Remember, it’s a risky one which might get you dreadfully hurt.

There is also another difficulty with the changing the mean strategy into the nice one. If you have adopted the mean strategy, then you have also already adopted a tactic of mendacity. After all, you didn’t need to stay in to wash your hair, did you? And you do find your suitor very attractive – you just don’t want him to know it. Yet, at any rate. His presents fill you with delight, but you can’t show it. You hope he will decode your behaviour so that you can maintain your posture of relative indifference, and thus the upper hand and power in the relationship, whilst throwing him enough bones to keep him interested. But what happens if he doesn’t understand what your true feelings are? What occurs if he takes your indifference at face value? Well, he will probably either give in and leave you alone, but more likely – as he is smitten with you – he will start to adopt the mean strategy himself to avoid getting hurt any more, or out of a desire for revenge, in which case, your relationship is heading for the rocks. Being less than honest destroys trust. You might even doubt those whose motives are honourable, because you figure that if you are lying, then they probably are too.

The boy in such a game is, in fact, in a Catch-22 situation. This is because, as a potential suitor, he has to show himself to be a powerful, manly individual who can take charge – this is one of the tests that the princess is setting him. What does it look like if he accepts all his princess’s caprices and caves in to all her demands? He looks weak, and possibly even needy. Indeed, neediness can arise in normally non-needy people who are very much in love when one partner continually inflicts the mean strategy on the other by withholding affection. This means that the boy is almost obliged to meet the mean strategy with the mean strategy at some point in time in order to avoid looking spineless. If the girl does not flip quickly to the nice strategy at this point, things are not looking good.

All this goes to help illustrate how it can be that there are lots of successful, interesting and good-looking people around who seem incapable of finding romantic happiness and a stable loving partner. As a consequence, they are unhappy and lonely. Being afraid of losing romantic games means that you have little possibility of really winning them in any meaningful way. Naturally, all this is a law of averages and there are delightful, non-mean, wonderful-looking girls and boys, just as there are hideous specimens with nothing to recommend them who should be grateful for the slightest interest in themselves but who nonetheless behave in an appalling manner when there is any.