Game Theory

   Is love a gamble or can we assign a more definitive interpretation?

According to Shakespeare, love is merely a madness, but that shouldn't stop someone adept in mathematics from imposing some reason on it; since love is just a game and mathematics contains a perfectly good theory of games, let’s start there?

Let’s think about the initial phase of courtship, in particular the giving of gifts. Giving presents is an integral part of the early stages of love and any relationship, not only for humans, but for many animal species too.

Often it's the male that offers the gift; for a female, the cost of hooking up with a male can be high because it might lead to an unwanted pregnancy, or at the very least, a failed relationship. These are always possibilities, and it is for this reason that she has to be choosy about her partners, so usually it's up to the male to make the running and to do the persuading.

A small gift can give her valuable information about the male's intentions and of his "quality" ~ but the male has to be careful, too.

If he offers a cheap gift (in terms of effort or in monetary value) the female may not take him seriously, or may even mistrust his intentions.

If he offers a valuable one, she may simply take it and run, without giving him the everlasting love that he desires. So, what is the right strategy?

This is nothing more than simply a classical two-player game consisting of a sequence of moves: he offers a present, cheap or expensive according to how he rates her. The female, for her part, decides whether or not to accept the gift, and whether or not to let the relationship, erm. . . develop. It would not be unknown, for instance, for the male to desert the female not too far down the line, maybe leaving her with one or three children to look after and raise all on her own.

So what is the best strategy?

That, of course, depends on various other things, for example how attractive you are. What "attractive" means for sure can be hard to pin down, and no-one really knows exactly how attractive he or she is to a prospective partner. You can make a good guess of course, based on previous experience and results. If you've had a lot of admirers in the past, then chances are that you'll be attractive to the next one, too. Perhaps we could assign to each "player" a probability that the other will find him or her attractive.

The best strategy will also depend on what it is that you actually want. In the language of game theory, what "payoff" does each player get from the various possible (continuing with probability terminology) outcomes?

A male will always get a positive payoff from the simplest of relationships, but that payoff will be higher when the female is attractive. If she's unattractive he'll likely maximise his payoff by legging it and leaving the relationship early. The female only gets a positive payoff if she enters into a relationship with an attractive male who then stays around to assume family responsibilities and help with child care. In all other cases - an attractive male deserting her, an unattractive male staying, or an unattractive male deserting - she gets a negative payoff.

In one study, the objective was to determine the Nash Equilibrium, so-named after the mathematician John Nash (made famous in the film A Beautiful Mind). Such an equilibrium exists if the strategies adopted by each player balances the other out in such a way that neither has anything to gain by making changes to his or her strategy.

One trend emerged from this study that was important to males, both attractive and unattractive: give a gift that's reasonably expensive to you but worthless to the female, in a material sense, and you're in with a good chance while minimising your risk.

By offering a reasonably extravagant gift the male signals that he rates the female highly, and that he's got spending power. At the same time, the female will only accept it if she’s really interested. In this way, the male balances the cost of the gift by reducing the risk of falling for a "gold digger". An extravagant gift, for example, could be an expensive night out: it costs the male, but is distinctly uninteresting to the female if she doesn't value his company.

So is this a sure-fire way of making for a successful relationship?

Well, unfortunately not; reality is often more complicated than that and since there are perfectly reliable means of birth control in this modern age, the risks attached to pregnancy (getting knocked-up) are significantly diminished to the extent that they are, to all intents and purposes, removed. This leads to the somewhat huge complication that the gender roles can be turned upside down.

Also, different people may value gifts differently: while one female may be impressed by the offer of a Mercedes Benz, another may be positively put off and enraged by such a pretentious gift. Some females may prize a "worthless" night out even in the company of an unattractive male, and worse, there will be many, both male and female, who do not even play fair. Some females for instance may chose one type of male for child care and another type for brief romantic encounters, thereby having the best of both worlds. And some males, may try to take back their gifts when the flame dies down to maybe use on another unsuspecting female.

There can be no doubt that game theory can give a valuable insight into the evolution of relationships and certain courtship behaviours.  But, methinks, to completely unravel the tangled web of the subject of love, there may be a requirement to take a long and searching look into the theory of chaos.

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~ m8ed