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 A Beautiful (Group) Mind: The Nash Equilibrium and Improvisation R. Kevin Doyle The recent film version of “A Beautiful Mind” invents an event in John Nash’s life to help explain his Nobel Prize Winning concept, the Nash Equilibrium. Nash and three friends are sitting in a bar when suddenly a beautiful blonde and three other women enter the bar. All four men want to get laid. Selfishly, all four men want to go after the blonde. Nash, however, has an epiphany. He realizes that if they all go after the blonde, at least three of them won’t succeed. If one of them goes after the blonde, and the others go after the three other friends, they won’t succeed because the other three women will feel like second choices. However, if none of them go after the blonde, they will increase their chances with the other three women and, thus, have a greater chance of achieving their ultimate goal. In this final scenario, none of the men would benefit from changing their own strategy unless the other men changed their strategy first. This state of strategic balance is referred to as the Nash Equilibrium, and has been used to help explain everything from small market economics to mutually assured destruction. It is a central concept in an interdisciplinary approach to human behavior called Game Theory. For the sake of this field, games are described as “a scientific metaphor for a much wider range of human interactions in which the outcomes depend on the interactive strategies of two or more persons, who have opposed or at best mixed motives.” I believe that Game Theory in general, and the Nash Equilibrium in specific, can be used as a rational basis for some of the established “rules” of improvisation. One of the main improv concepts explained by Game Theory is the idea that better scene work can be achieved by working for the good of the group rather than the good of the individual. In order to demonstrate this idea, we need to visit the theoretical Really Selfish Improv Company (RSIC). For Game Theory to be a useful way of describing player interaction within improv scenes, there must be some sort of individual payoff. Since the easiest payoff to measure is the laugh, we will use this as the payoff in this example. Thus, the RSIC has been performing laugh-oriented improv scenes for years. Each member of the company wants to generate the maximum number of laughs for her or himself. They know their audience fairly well and can, with reasonably certainty, makes a scene destroying comment that will get a guaranteed laugh. As a result of this, at any given moment in a two player scene, either player can keep the scene alive and “true” and risk not getting a laugh, or destroy the “truth” of the scene by getting their sure-fire laugh. Alas, if they both go for the laugh at the same time, their destruction of the scene will appear sloppy and undermine their ability to generate a laugh. Let us take a look at a chart that describes a moment in the life of the RSIC:
In other words, it is in the interest of the selfish players (who, as you recall, want the maximum number of laughs) of the Really Selfish Improv Company to make choices that preserve the flow of the scene and allow for more potential laughs than to go for the one big laugh on their own. In essence, if each RSIC player works in the best interest of the group, as opposed to themselves, they will ultimately have better individual payoffs. The concept of abandoning individual control for the good of the group is drilled into many improvisators’ heads from their first class, so this might not come as a huge revelation. However, this particular Nash Equilibrium provides a rational basis for this concept. There are, I suspect, other basic rules of improvisation that can be rationalized using Game Theory. Indeed, the RSIC example really only examines one form of payoff for an individual improvisator: laughter. There are many other potential payoffs that lead to somewhat different conclusions. However, at this point in time, I am in the process of examining many of the basic “rules” through game theory for use in future writing. I plan to develop the RSIC example, and propose several others, in the coming months. For the time being, let me move away from scene theory and show one way Game Theory can be used in running the business of an improv company. Game Theory offers a rational explanation of why it is economically important for different improv groups in the same market to establish their own identity. Let us assume that the RSIC exists in a town with a second improv groups – the One Act Wonders (OAW). Their shows both happen on the same night in different venues. There are 100 people who go to see improvisation. Of these 100, 50 want to see fast, funny short form, 30 want to see improvised one act plays, and 20 want to see edgy improvisation. Let us take a look at a different chart:
Anecdotal evidence from the major improv markets in the United States suggests that the so-called “major” groups in each city have certain identities that match up with specific fan bases. For example, in the Chicago improv scene described in “Whose Improv is it Anyway,” the different groups have distinct identities and, largely, distinct audiences. While the desire to do something different might spring up for artistic reasons, the success of that new group depends largely on its ability to attract an audience that is distinct from the other existing groups. In both the RSIC scenario and in the multiple troupe scenario, choices made by the individuals within the equation ultimately benefit everyone involved in the equation – or, at least, allow everyone a greater payoff than should they all act in their own self-interest. Since in competitive situations, whether on stage or between troupes, each player wants to “win” the game, an understanding of Game Theory can help improvisators choose strategies that result in the best payoff for everyone involved. Sidebar or comment: For more information on Game Theory, visit Roger McCain’s wonderful web site, Strategy and Conflict: An Introductory Sketch of Game Theory. | |||||||||||||||||||||||||||||||
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