by Andrew Trees
THE GAME OF LOVE
The use of market-driven thinking is not the only way to apply mathematical rationality to the world of dating. Another area that has gained increasing prominence in understanding animal mating, including the human variety, is game theory. Nobel Prize-winning mathematician John Nash, the subject of the movie A Beautiful Mind, made his most important contributions in the area of game theory. He came up with something now known as the Nash equilibrium, which allowed game theory to be applied to a much wider variety of issues, including dating (although no one would get around to applying it to that until the last couple of decades).
Game theory is a branch of applied mathematics that was initially used primarily in fields like economics and political science. There are a huge variety of “games” that one can play—zero sum and nonzero sum, symmetric and asymmetric, continuous and noncontinuous, cooperative and noncooperative, simultaneous and sequential to name just a few variations—but we’re not going to worry about those complexities; instead, we’re going to explore only a few areas where game theory might actually offer some practical assistance when it comes to dating.
First, some good news for women. They set the ground rules for the game. As I hope the chapter on evolutionary psychology proved, men want to have sex, and in general they want to have it more often than women do. Because of this, women are in the driver’s seat. Game theory can demonstrate this through an examination of a question we explored earlier: why monogamy? Using the techniques of game theory, biologists have been able to reduce that complicated question to four linked propositions that determine whether a society will be monogamous or polygamous. Without further ado, a quick and dirty guide to the mating game, compliments of Matt Ridley’s wonderful book on sex and evolution, The Red Queen:
1. If females are in a better situation by choosing a monogamous relationship, a monogamous society will be the result;
2. UNLESS men can force women into polygamous relationships (the “grabbing the woman by her hair and dragging her back to the cave” school of dating);
3. If females are not in a worse situation by choosing men already paired with a woman, a polygamous society will be the result (the “it’s better to be the second wife of Brad Pitt than the first wife of Homer Simpson” school of dating);
4. UNLESS the females with mates can prevent their mates from adding an additional mate (the “don’t touch my man, or I’ll rip off your hair extensions” school of dating).
Did you see the role that men played in all of that? You have to look closely—male agency makes a brief appearance in proposition #2. Other than that, it’s girl power.
Of course, we already know that we live in a monogamous society, and all sorts of variables creep in that quickly complicate any simple scenario. Take, for instance, the issue of sex. Women willing to accept a short-term relationship can probably attract a much higher quality mate than if they hold out for a long-term commitment. But a single woman can’t completely alter her market value simply by withholding sex, because she is not only trying to attract a man but is also competing against other women.
Another classic game can illustrate the problems that this sexual uncertainty adds to the equation. Imagine that a group of hunters are chasing a stag. If they all work together, they will kill the stag and share in a vast quantity of meat. But there is a chance that they will fail to catch the stag. Then, no one will eat. A hunter can also desert the stag hunt and kill a rabbit. If he defects early, he has an excellent chance of killing one, although it won’t be the meat bonanza of the stag hunt. If enough hunters defect, the stag will definitely escape, and only those early defectors who went after the rabbits will eat. The game outlines the difficulties of cooperation.
Now, imagine a similar situation with women who are all pursuing a high-status male with little interest in a long-term commitment. Only these women face an added difficulty—they will not share in the spoils of the hunt, which makes cooperation among them virtually impossible. If they all agreed to abstain from sex with him, they could very likely force him to choose a long-term partner. But some of those women will know that they are unlikely to win the prize. They might be happy to have a short-term liaison with the man (the equivalent of going after a rabbit), rather than nothing at all. So, while a woman can exercise great power over her suitors by withholding sex, she is not doing this in a vacuum, and there are plenty of women around her who will choose to play the game differently.
GETTING INTO THE GAME
As with analyzing dating as a market, people must first accept that there is an element of strategy in their own dating—another direct blow to the romantic story line, which insists that love is spontaneous and largely impervious to manipulation. Some people are reading this now and thinking, “I don’t play games.” You may very well believe this is true, but that is simply one more move that one can make in any game situation. By saying you don’t play games, you are signaling to others that you have certain traits (trustworthiness, sincerity, etc.) that make you more attractive. You may also be trying to rule some games out of bounds (for example, you may be signaling that you won’t tolerate deception). However, all but the most obtuse among us will admit that there are certain moves in the game of dating that we don’t make, no matter how much we claim not to believe in games. For example, no one wants to look desperate. We all know that on a first date, no matter how well it is going, we don’t blurt out that we think we might be falling in love or that the other person is “the one,” even if we have glancing thoughts in that direction. It’s a supremely bad move, more likely to signal that you are not a valuable dating partner.
There are an almost infinite number of moves in any encounter, but some basic ones frequently come into play. Men tend to deceive women about how committed they are, and women try to counteract that by imposing courtship costs. Some women even resort to what a game theorist would call the ultimatum game when they tell their partners that they have to be married (or engaged) by a certain date, or the relationship is over. Others try to impose strict rules for the games that are allowed by joining dating sites that have values built in, such as conservadate.com or singleswithscruples.com (which explicitly markets itself to people who are “tired of games”!).
My own personal favorite is the self-deprecation gambit. The appeal of the anti-appeal. In other words, you are such an attractive candidate that you can dispense with all the usual self-marketing, actively denigrate yourself, and still appeal to the opposite sex. This is more common that you might think. Just take a look at They Call Me Naughty Lola, a hilarious book on the self-immolating personal ads people have placed through the years in the London Review of Books. A few choice examples:
“Shy, ugly man, fond of extended periods of self-pity, middle-aged, flatulent, and overweight, seeks the impossible.”
“Blah, blah, whatever. Indifferent woman. Go ahead and write.”
“Unashamed triumphalist male for the past forty-six years. Will I bore you? Probably. Do I care? Probably not.”
Not only hilarious, they illustrate Zahavi’s concept of the high-cost signal from the chapter on evolution. Only people with charm and looks and talent to burn (as well as excellent senses of humor) can afford to be so self-deprecating about themselves—which is a useful lesson for the rest of us: the soft sell is more effective than the hard sell.
For those interested in cleaning up the game of love, one simple change can help eliminate a great deal of bad behavior: increase the length of the game. That’s what a political scientist did when he invited experts in game theory to submit computer programs to play against one another in a game known as the prisoner’s dilemma. Several dozen programs were submitted, and they “played” for hundreds of rounds. The winner? The shortest program submitted—a mere five lines—which its creator dubbed “Tit for Tat.” The program did exactly what you would expect. In its initial encounter with any program, it would cooperate. In all future encounters, it would do what the other
program had done in the previous encounter. If the other program cooperated, it would cooperate. If the other program acted selfishly, “Tit for Tat” would behave selfishly. This simple idea of rewarding good behavior and punishing bad behavior bested every other program. To create a similar situation in the dating world, though, you would need to have the same two people “play” (i.e., date) each other multiple times. Under these conditions, people would quickly clean up their behavior because deception and other bad behavior would simply be punished in the next round.
Unfortunately, dating is not like that. The partners in any game are constantly shifting. But you could still achieve similar results if you had good enough communication. When people can communicate the past behavior of others, they can form networks of trust and shut out players who rely on deception. Imagine if each of us was given a rating based on our dating histories, similar to the buyer and seller ratings on eBay. If someone behaved badly, he or she would find it increasingly difficult to find anyone to date. When people lived in one place for most of their lives, gossip essentially served this function and helped impose a standard of behavior, and some Internet sites are now starting to adopt this concept, although it is far from foolproof since users can simply move to a new site. If one dating Web site ever dominates the way that eBay does with online auctions, it will have the power to improve the behavior (or at least the honesty) of men and women when they date—more so than anything since Moses came down with the Ten Commandments.
THE DOWRY GAME
While all this game theory may be interesting, some of you are probably wondering right about now, so what? Is there some more practical advice that game theory can offer? Well, yes, actually there is. For example, it can finally provide an answer to that age-old question: how many people do you have to date before you meet your true love? The answer: twelve. That’s right. A nice, round dozen. Not too difficult, right? Okay, yes, I realize you are going to need more convincing than that. Many of you have dated far more than twelve people and are still no closer to finding a partner than you were when you were the age of twelve. Others are probably outraged that I would even put a definitive number on such an amorphous task. Besides, what’s so special about the number twelve? It’s not as if Cinderella crossed that threshold, which, by the way, is one of my pet peeves with the romantic story line. The storybook lovers always seem to meet the right person very early on, leaving the rest of us poor schlubs feeling that taking a long time to find love is itself another sign of failure.
But back to the lucky number twelve. How in the world can we possibly arrive at such a precise number? To understand that, I’m going to ask you to play a game. Mathematicians have called this game by a variety of names. We are going to play the version known as the dowry problem. Let me set the scene. You are the king’s most trusted adviser. He wants to find you a lovely bride (or groom), but he also wants to make sure that you truly are as wise as he thinks you are. So, he arranges a challenge for you. He sends out his minions and finds one hundred of the most beautiful women in the land. He then provides each of them with a dowry, only he doesn’t provide them with the same dowry. Each woman has a dowry different in value from all the other women. Your challenge is to pick the woman with the highest dowry. If you succeed, the beautiful bride and the sumptuous dowry are yours to enjoy, and your place at the king’s side is secure. If you fail, he’s going to chop your head off. Oh, and one more thing, you meet the women one at a time, and once you have dismissed a woman, you can never call her back. Ready? Let’s play.
Being the brilliant adviser that you are, you probably have already figured out the math for all of this. I, of course, am terrible at math and am relying entirely on the excellent article by Peter F. Todd and Geoffrey F. Miller called “From Pride and Prejudice to Persuasion: Satisficing in Mate Search,” which can be found in Simple Heuristics That Make Us Smart. Once you crunch the numbers, you realize that your best chance is to pass on the first thirty-seven women and then pick the next woman who has a higher dowry than any of the women who came before her. Mathematicians have dubbed this rather obviously the “37 percent rule.” By seeing the first thirty-seven women, you will give yourself a 37 percent chance of choosing the highest dowry. Not the greatest of odds when you are under the threat of having your head chopped off but a better percentage than you will get with any other number. If the king lets you play the field a little bit, you can improve your chances dramatically. If you can keep one woman while you continue your search, you can increase your odds of finding the best dowry to 60 percent. Not too shabby.
Those of you who feel a little letdown about the 37 percent rule, raise your hands. Thirty-seven is nowhere near the twelve I promised. Dating thirty-seven people sounds exhausting. Well, apparently Todd and Miller agreed with you, and they set about tweaking the game in various ways to see if they could find a better way.
Instead of the 37 percent rule, you could try the “Take the next best” strategy. Of course, you are going to have to give up on the idea of “the one.” If your sole criteria is trying to find the single-best mate, you’ve got to stick with the 37 percent rule. But if you are willing to accept anyone in the top 10 percent, you can follow the 14 percent rule. This rule works as you might expect. You pass on the first fourteen women (or men) and then choose the next woman who is better than those first fourteen. If you do this, you have an 83 percent chance of ending up with someone in the top 10 percent. If you are willing to accept anyone in the top 25 percent, you only need to look at the first seven women and then choose to have a 92 percent chance of success. Let’s say you are unlucky in love and just want to avoid marrying someone in the bottom 25 percent. Then you only need to check out three women, and you will have less than a 1 percent chance of ending up with a loser. That may not sound all that great, but the 3 percent strategy still does a better job of avoiding losers than the 37 percent rule, which has a 9 percent chance of landing you with someone in the bottom 25 percent. While the 37 percent rule provides the best chance of picking the best person, it does worse at almost everything else, including picking someone in the top 10 percent or even the top 25 percent. It also results in a lower overall average mate value.
Running all the numbers, it turns out that the best strategy is the 10 percent rule, which results in the highest average mate value, a high chance of landing someone in the top 10 percent and a very high chance of landing someone in the top 25 percent. To give you some sense of how much more effective the 10 percent rule is than the 37 percent rule, compare the average mate values. The 10 percent rule gives you an average mate value of 92 out of 100 versus an average mate value of 81 out of 100 if you use the 37 percent rule (and you have to date a lot fewer people!). The 10 percent rule isn’t particularly onerous. You only need to date ten people from a field of one hundred. That is lower than the twelve I originally promised. Of course, you are likely going to have to date more than just those ten. Remember the way the game works. The 10 percent rule means that you have to pass on the first ten people and then choose the next person who comes along and is better than the first ten. On average, you will end up working your way through roughly thirty-four potential candidates.
Of course, there are probably some indefatigable daters out there who think that one hundred people is a rather paltry total: the dating decathletes among us who are perfectly happy to date one thousand people if it improves their chances of finding true love. If you are choosing among one thousand women (or men), the 37 percent rule means that you will no longer be doing anything but dating for the foreseeable future. If you are willing to accept someone in the top 10 percent, though, you only need to apply the 3 percent rule for a 97 percent chance of success. And the numbers are even better if you are willing to accept someone in the top 25 percent. After running the game for numbers ranging from one hundred to several thousand, it all boiled down to one simple rule: try a dozen (Cresswell dubbed this the twelve-bonk rule, bonk being a British word for . . . well, I
’m sure we all know what bonk means). Todd and Miller found that this number provided excellent results no matter how large the sample size. As they aptly put it, “A little search goes a long way.” We may still choose the wrong person, but the “try a dozen” rule shows that our mistakes are probably not from lack of trying.
Although I have yet to meet anyone who has explicitly used the twelve-bonk rule to choose a partner, the anecdotal evidence suggests that some of us subconsciously follow a method roughly analogous to it. For example, a number of people said that they viewed finding the right person as a simple numbers game. They just had to ensure that they met enough people in order to find the right fit. I realize this contradicts to some extent what I said earlier about too much choice, but it is very different to date several dozen people over the course of several years than it is to scan hundreds or even thousands of online profiles in the course of a few hours. The surprising thing was how often the numbers roughly correlated with what the twelve-bonk rule predicts. One woman decided to get serious about meeting someone and went on thirty-eight dates over a two-year period before finding Mr. Right, which is very close to the average predicted by the “try a dozen” rule. Another woman inadvertently ran her own modified version of the dowry game, albeit without the fatal consequences. She went on a hundred first dates, ruthlessly culled from that list ten men for a second date, ruthlessly culled again and went on a third date with three men. She ended up having a long-term relationship with two of the men, and she married one of them. I also found a variety of other people who had used methods roughly analogous to game theory. One systems engineer even described his marriage as a “system deployment,” a statement that positively drips with romance.