After a long night of tossing and turning last week, I decided to pick up a magazine to lull myself to sleep. Unfortunately, the only stack in my fraternity’s bathroom was of Playboys, and the obvious thing to do with those would only serve to keep me up even longer. Then I remembered what my dad would always tell my mom - he likes the articles. So I decided to give it a go and look away from the busty cowgirl on the left and the not-so-innocent Catholic schoolgirl on the right, and focus my eyes on the article in the middle of the page [Playboy, March 2008, The Look of Love, pg. 99].

While most of the article (read: most important part of the article) dealt with how to properly pick up signals from girls, my nerdy Cornellian self became engrossed by the section which proposed a mathematical model for marriage. Specifically, the author proposed a game theory problem regarding the decision of which partner to propose marriage to. Each player (person) wants to maximize his or her payoff, which is abstracted to be the strength of his love for his spouse. In other words, each player Pi, out of the set of all people willing to marry him or her, wants to marry the one he or she likes the best out of the set. However, the circumstance is complicated by the fact that in a monogamous society personal evaluation is sequential and not parallel. In other words, in order to evaluate his affection for another person, the player has to date him or her, and he or she can only date one person at a time. This poses a problem. If the player proposes to too early a partner, he or she may not have yet met someone better. Therefore, proposing too early leads to a sub-optimal expected payoff. Likewise, a player should not propose too late, for by the time he or she decided to tie the knot, he or she may had already dated and broke up with “the one.” In this case, he or she has to settle for someone sub-optimal because his or her perfect partner is in the past. This model assumes that a person will not take back anyone that they had already dated and broken up with. The author, not going into mathematical detail or empirical methodology, cites Miller’s The Mating Mind proposing an optimal strategy dubbed “the 37 percent rule.” The strategy states that to maximize expected payoff, the player should date 37% of his expected partners, remember how much he or she liked his favorite of the bunch, and then marry the very next partner whom he loves at least as much.

Of course, not everyone has an online subscription to Playboy (I keep one around purely out of scholastic pursuits such as this, I swear!), so instead of focusing on the above model, I instead used it to springboard to another article which I found interesting. Authored by Williams, The Mathematics of Dating: Applying Game Theory to Win a Spouse [http://www.associatedcontent.com/article/465911/the_mathematics_of_dating_applying.html] deals with a more advanced model of dating and marriage. Whereas the Playboy article assumed what Williams terms “closed players” who will not date a person more than once, Williams’s model introduces another type of player - an “open player” - who is open to dating his partner again after they have dated other people. This model complicates players’ strategies even further. While breaking up with an open player carries less risk since another round of dating with him or her is possible, a player must be more sure when breaking up with a closed player.

On his path to optimal strategy, Williams proposes multiple possible strategies that at first glance seem to be optimal. Interestingly enough, positively-connoted strategies such as “Idealistic,” “Acceptance,” and “Young Love” strategies proved to be the worst. The top 3 were “Desperation,” “Stalker,” and “Nagger.” A Desperate dater will go down his or her list of favorites and propose to them in order until someone (anyone) says yes. If no one does, he or she will propose to every person he or she dates. A Stalker, on the other hand, keeps proposing to his favorite partner until he or she accepts (for example, if that person’s favorite person marries off and our Stalker is the next one on the list) or gets taken off the market (marries off). A Nagger - who proves most adept at this dating game - combines the two strategies by desperately proposing to everyone on his list in order every time he goes on a date. This way, he or she can come back to Open Players who rejected him or her (Desperate dater’s weakness), but not get stuck on one person (Stalker’s weakness).

This problem and the derived set of strategies - in particular the optimal Nagger strategy - is an interesting thought experiment and an example of applicability of game theory to everyday life. It deals both with networks and game theory. Specifically, the problem resembles perfect matching, wherein each person has a valuation (in this case his or her affection) on a product (dating partner). The difference is that in this case the edges (compatibility) don’t get drawn in until the two nodes (people) had dated. Furthermore, whenever a pair is matched (married), it gets deleted from the graph. In these ways, the graph is ever-evolving, with nodes appearing, disappearing, and edges being created all the time - complicating strategy.

In sum, if the dating game at times seems too much - nag. Go to your ex’s and propose to them in descending order of affection. And if (more accurately when) they all decline - no worries. Next time you go on a date with somebody new - simply propose to all of your ex’s and the new (boy/girl)friend all over again. Cheers.