The Mathematics of Dating: Applying Game Theory to Win a Spouse

Of all the things mathematicians ought to keep their rational hands off of, you'd think searching for a spouse would near the top of the list. But then, you'd miss out on these excellent strategies for winning the Game of Love.

The object of the Game of Love is to marry the best mate you can. The only rule is that everyone can choose to accept or decline a marriage proposal (the following strategic analysis doesn't apply to arranged marriages or "shotgun" marriages). I make a few assumptions to begin with.  

The First: Free will trumps fate in this model. I assume there are a vast number of people that a given person (a.k.a. "player") could marry and be happy with. Some would make the player happier than others, but there certainly isn't a single "Soul Mate" that each person must find - less they be doomed to loneliness forever. I think this assumption make this model more realistic.

The Second: no one will accept a marriage proposal from anyone who doesn't meet their standards (ie: no one will say "yes" to anyone who isn't at least "okay" in their book. Mary would rather stay single forever than accept a proposal from Mr. Wrong).

The Third: everyone will accept a marriage proposal from the best person they think will marry them (ie: Mary will always say "yes" to the current man of her dreams).

The Fourth: everyone will decline a marriage proposal if they know they will get a better offer (ie: Mary will say "no" to Mr. Okay if she knows Mr. Perfect will propose to her tomorrow).

The Fifth: there is no way for one person to be sure the other person will accept or reject their marriage proposal, aside from actually proposing.

The Sixth: no one is waiting around in this game. Everyone is busy looking for the best mate they can find. Just because someone would accept your marriage proposal today, doesn't mean they'll accept it tomorrow.

Finally: in this model of the Game of Love, any player may propose to any other player any number of times. When two players get married, they are both "out of the game."

With these seven assumptions, let's begin our analysis.