What if there were a principled way to go about social interactions, to decide whether a romantic relationship will work out, or how to decide who gets to decide the evening’s entertainment? Well, there is. Classical economics was hit with a dramatic change in its method analysis a little over half a century ago, when John von Neumann and Oskar Morgenstern famously formulated game theory. Since then, it has been applied to an extremely wide variety of topics and fields – prisoners facing time, organisms facing extinction, and lovers overwhelmed by Valentine’s Day conundrums.

Recall the scene from A Beautiful Mind. Four men are sitting around a table in a pub and surveying the possible dance partners across the floor. Just as they start talking, a group of five girls walk in and the men start gawking – at one blonde in particular. But one man, an economist, tells his friends not to go for the blonde in fear that they will box each other out, and then get the cold shoulder when trying to go for her friends as seconds. The economist, John Forbes Nash (played by Russell Crowe), tells his friends to forget the blonde and move in directly for her four friends. This way, everyone does “what’s best for himself and the group,” leaving everyone without competition and happy.

The problem is, the solution is neither stable nor efficient (loosely translated as value maximizing). The odds are Nash is just making sure he has a clear path to the blonde without interference. The incentive to cheat the agreement makes the situation a weak characterization of Nash Equilibrium, where no player can benefit by changing only his strategy, ceteris paribus. The strategy reached by Russell Crow’s character is not an optimal solution to the game described because the men, as a whole, could attain a much higher aggregate value by appointing one person, or agreeing in some other way, to go for the blonde.

A game, specifically pertaining to the success in relationships, which has been heavily studied by game theorists is one called the “Battle of the Sexes.” The “Battle of the Sexes” is a coordination game, where the object is to follow the other players, with asymmetric payoffs. Allow me to formulate the problem like this: Bobbie wants to watch Basketball (like Friday’s game against Bowdin at 7:30) and Gerry wants to see Gospel (like Friday’s performance at 8:00), but they will only derive their benefit by doing the same thing together and neither of them have any minutes to call each other.

Here, we have two Nash Equilibria. If they go to basketball, neither has an incentive to switch to Gospel individually, but Bobbie derives considerably more benefit, and vice versa for Gospel music and Gerry. The interesting question now is: How is one equilibrium chosen over another, assuming the aggregate benefit is the same in both cases?

Bobbie and Gerry did not set up in advance which they were going for, so each finds themselves at 7:25, Friday evening, wondering which place to go to – Freeman or Crowell. Game Theory’s answer is something called a mixed strategy. In a mixed strategy, each player looks at each player’s relative payoff for each strategy and maximizes her expected utility by choosing each activity with some probability. Thus if she really wants to go to the basketball game, then she will, with higher probability, go there, taking the chance that her partner will not show. If she knows her partner really values gospel music, then that, too, will change the probability. Once this probability is determined, each partner should flip coins to decide where to go.

It is somewhat naïve to imagine that each player will derive absolutely no benefit from her favorite activity if her partner is a no-show. To make the game more realistic, assume Bobbie will still have fun (though less) going to basketball alone, and Gerry will still have fun (though less) going to gospel alone. This way, an incentive is created to forgo coordination when it is overly costly or non-equitable. So when it comes down to it, the measure of a relationship can be expressed by the frequency with which the game can be replayed and the relative value between coordination and doing your favorite activity.

It may seem somewhat unsympathetic to talk about valuing relationships in this way, but I urge you to remember a key tenet of economics: everything has a price. In fact, chances are you put a price on your relationships every day, and even more so as Valentine’s Day approaches.

As we prepare for the day of love, remember these important lessons: always convince your friends you are the rational choice for the best dance partner, make plans with your partner or have a fair coin along, and even if quarters can’t buy you love, something valuable’s got to.

About Andrew Dermont

Andrew Dermont organized the overhaul of the Argus website. He is now the Blargus Editor and oversees the publication of all online-specific content.