Good news for all women who will not be rushed by a potential Mr Right: mathematicians have now proved you are doing exactly the right thing. Having a long courtship really is the best way to weed out the bad guys. The very idea that mathematics can cast light on affairs of the heart may seem preposterous, but it has a venerable history. Even before Newton wrote down his famous laws of motion, the 17th century English philosopher Thomas Hobbes suggested that human behaviour might be predicted on the basis that our lives are in the grip of various "appetites" and "aversions".
The challenge has been to find the right kind of mathematics to capture the essence of the problem without simplifying it to the point of irrelevancy. In the case of the analysis of courtship, researchers have turned to a branch of applied mathematics that with a name that belies its significance: game theory. Invented in the 1920s, game theory acquired its moniker from its use in finding the best way to play games in which it is unclear what opponents are thinking. At first, mathematicians contented themselves with so-called "zero sum" games, where one person's gain is exactly matched by the other person's loss, such as poker. In such games, it emerged that there is a recipe - the Minimax Theorem - which gives the biggest payoff in the worst circumstances.
The real challenge, however, lay in finding a similar recipe for the far more common - and important - case of games which aren't zero-sum. One such "game" is nuclear war, where choosing the wrong strategy can lead to mutual disaster. With impeccable timing, the recipe for optimal strategies was found during the depths of the Cold War by John Nash, an American mathematician (made famous by the 2001 film A Beautiful Mind), who was awarded a Nobel Prize for his discovery.
Since Dr Nash's breakthrough, game theory has found uses in a host of disciplines from psychology to sociology and evolutionary biology, with the most interesting applications often involving all three. One such is the game theory of courtship, as investigated by Prof Robert Seymour of University College, London, and Peter Sozou of the University of Warwick, Coventry. Courtship seems tailor-made for game theory: neither males nor females really know what is going on in the other's mind (even if they have their suspicions), while both stand to win or lose substantially if they make a bad choice. The twist is that the two "players" may have very different views of what counts as winning. For the female the objective is clear: find someone who is both likely to provide a healthy family and to stick around. The male, on the other hand, may not be keen to do either.
So what's a girl to do? To find out, the researchers applied Dr Nash's methods to identify a strategy that minimises the risk of ending up with a bad guy. Sure enough, it confirms the age-old wisdom that putting the man off for a while is a good thing - as the bad guys will not wait, while the good guys are prepared to be patient. What the equations do not reveal is how long men should be kept waiting, in light of the fact that not even good guys will necessarily wait forever. Deciding on the length of courtship is thus a matter of judgement - which isn't much help for women of a certain age.
But for men wanting to come across as good guys, game theorists have now confirmed another long-held belief: do not mess your new date around - she will not stand for it. The finding emerged during research into the importance of trust using a classic game theory set-up called the Prisoner's Dilemma. Two friends are arrested for a crime, put in separate cells by the police and each offered a pardon if they implicate the other. If they both stay silent, they will both go free - but if one of them breaks ranks and talks, he will get a reward, while the other goes to jail for a long time. So what should you do?
The Prisoner's Dilemma is notorious for not offering any simple answers - especially if it is repeated with the same players, affecting their trust in each other. At Ohio State University, Prof Robert Lount and colleagues have carried out experiments in which students are put through repeated games of Prisoner's Dilemma to see what effect violations of trust had on their behaviour. Each student played the game with a computer dozens of times, during which the computer betrayed the student just twice. What varied between students, however, was whether the computer betrayed them early on, later or not at all.
The results, reported in the current issue of the Personality and Social Psychology Bulletin, show that timing was crucial. Students whose trust was betrayed early on were far less likely to trust the computer as the games progressed. In contrast, students who were betrayed later were perfectly happy to continue trusting the computer. During the experiment, the students were not aware they were playing a computer and were asked by the researchers to describe their feelings towards their "partner" during the game. Not surprisingly, those who had been cheated on early rated their partner as less trustworthy than those whose faith had been justified until later on.
The responses showed something else, however. Those cheated on regained some of their trust with time - but not to the level of those who were betrayed later or not at all. The experiments thus confirm in the lab what many discover ruefully in love: that trust broken early is never fully restored. Those who think otherwise are likely to find their relationships decidedly Hobbesian: nasty, brutish - and short.
Robert Matthews is Visiting Reader in Science at Aston University, Birmingham, England
