Home > Game Theory, Lessons > Game Theory and the Narrative #4, Battle of the Sexes

Game Theory and the Narrative #4, Battle of the Sexes

A Battle of the Sexes, in game theory terms, is a game where two players have no perfect solutions. They only have acceptable and unacceptable solutions.

The common example, from which the scenario derives its name, is this:

A husband and wife have agreed to go out for an evening. Neither can remember where they have agreed to go. They would both rather go anywhere together than be apart. The husband recalls they agreed to go to a boxing match, which he would prefer; the wife remembers agreeing to go to an opera, which she prefers.

In this scenario, the husband achieves maximum happiness in only one condition, going to the boxing match with his wife; and the wife only achieves maximum happiness at the opera with her husband. Neither achieves any happiness if they go their separate ways. In the end, there are two ‘best’ solutions. They both go to either the opera or the boxing match. Mathematically, it doesn’t really matter which, though of course to people it matters whose preference is observed.

In a narrative, we want to see protagonists aligned this way. We want all of the protagonists rowing in the same direction, but we don’t want them all perfectly happy about it. We want some to think they’re going the wrong way or at the wrong speed. Dissatisfaction is human, and to see it in our protagonists reaffirms their humanity. Sticking together despite their disagreements is part of what makes them protagonists. They are willing to sacrifice for the greater good. They get more satisfaction from going with the team than striking out on their own.

We can think about the Fellowship of the Ring. Merry, Pippin, Sam, Frodo, Gandolf, Aragorn, Boromir, Gimli, and Legolas often disagreed about how the should get to Mordor, but once a decision was made, they, while the Company lasted anyway, stuck together despite their individual reservations. Different characters determined the direction the Fellowship took, too. At different points Gandolf, Aragorn, and Frodo all pick a course and the rest follow.

For our heroes, being together is strictly better than any outcome where they are separated.

  1. Studnougat
    April 28, 2011 at 2:33 pm

    Muddying the waters in this regard is interesting. What if the husband only kind of wants to go boxing, but really doesn’t want to go to the opera? What if he is morally opposed to the opera (or insert task) without good reason? And how often in life do you GET to make a decision that maximized your own happiness, or alternatively, do we really know what will make us truly happy?

    • April 28, 2011 at 3:36 pm

      Exactly, if he hates the task, but hates the separation more, then the tension is pleasing to read (though, likely, not to experience). He gets some, minimum, satisfaction for do what she wants, but then, I can imagine, focuses so much on his own unhappiness, everyone is miserable.

      Ah, well. Economists would say every decision you make is an attempt to maximize your own happiness, and all of the game theories and all of the calculus is just trying to describe why people to the often ridiculous and apparently non-happiness-maximizing. That leads into your last point- much of economics and game theory focuses on rational actors with ‘perfect knowledge’. Perfect knowledge doesn’t mean complete omniscience but full awareness of the choices available at a given time. Chess is a game where you have perfect knowledge; poker is one where you don’t. Reliance on both rational actors and perfect knowledge is a weakness of these systems, which is why something like the dragon-slaying article was so interesting. It focused on large groups of people who, in the aggregate, act in a mathematically provable, and rational ways.

      Dudes who hate the opera might not fight perfectly in the math box.

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