John Nash, the Movie “A Beautiful Mind” and Game Theory
The Story-Telling, Game Theorist, Troubleshooter, and Common Sense Problem-Solver
Helping people to create better lives through efficiency, effectiveness, precision, self-awareness, Eastern Wisdom and game-based strategies
Q. I recently saw the award-winning film, “A Beautiful Mind,” about the game theory pioneer, John Nash. Can you tell me more about him and his ideas?
A. To begin with, it was this movie that piqued my interest in viewing and living life as if it is one big game. Game theory, the analysis of socially interactive human behavior patterns came before the public consciousness through this film which was a Biographical presentation on the life of John Nash. In the film, Nash is under extreme pressure to publish, but he wants to publish his own original idea. His inspiration comes when he and his fellow graduate students discuss how to approach a group of women at a bar. Some of the students proclaim that “every man for himself” is the way to go but Nash argues that a cooperative approach would lead to better chances of success. We know this as a win/win situation. Nash called it a non-zero-sum game*. From this event, Nash developed a new concept of governing dynamics and published an article on this. On the strength of this article, he was offered an appointment at MIT.
As you explore the many and varied elements of game theory and applied game thinking in all of my books you will often hear Nash’s name mentioned especially in relation to the term Nash Equilibria or Nash Equilibrium. In order to effectively use game-based thinking in sophisticated situations with skilled competitors or adversaries, it is important to understand this concept and how it came to be.
In 1948, John Nash, then a 21-year-old Princeton grad student was studying Von Neumann’s ideas concerning game theory. The question that came to his mind was, “what is the best strategy to use in a game when I am aware of what another person’s strategy is likely to be?” In the language of a mathematician, this would be described as “solving the problem of finding equilibria in a game where there is a potential for everyone to win.” A game where everyone has the potential to win and no one has to lose is called a “nonzero-sum game*.” Nash came upon this idea and a solution. Ultimately it would win him the Nobel Prize, almost fifty years later after he published a paper on his ideas. This paper was written just a few years after Von Neumman and Morgenstern published their book on game theory. Today Nash Equilibria* is one of the most important foundational ideas of game theory.
Let’s explore Nash’s ideas in greater depth. In any game, there is a consistency of the rules of play and of the strategies of the players that can be expected in a defined game. Experts in the study of games, game thinking, and game theory, have named this assumed consistency of rules and player strategies “equilibrium.” Many creative equilibrium concepts have been developed (most famously the Nash equilibrium) in an attempt to capture this idea. The question a student of game theory and game thinking might ask is this – “How can you turn a win/lose game into a win/win game?”
“Nash showed what the best response would be in a Win/Win nonzero-sum game but what of a win/lose zero-sum game. A game where there can only be one winner?”
He also showed that when addressing the question of equilibria in win/lose games one need not worry about what the benefit of winning would be for an opponent. All that was relevant was the strategy(s) the opponent might choose. Why is this so? The reason is that the opponent’s payoffs* are implicitly known in that they will always be diametrically opposed to yours! So in a win/win (nonzero-sum game*), when computing the “equilibrium strategies*”, you have to consider what the opponent’s payoffs are. On the other hand, in a win/lose (zero-sum) game you are not concerned with the payoff, only your strategy. This might have seemed a small distinction but for experts whose job it was to formulate game theory based strategies in war and in the marketplace this concept was revolutionary. It became clear that this slight difference could cause a decision maker to choose a different strategy than they might have if they did not possess knowledge and an understanding of the “equilibria” concept. Thus this approach became known among mathematicians as a “solution technique” and the effective strategies created through this type of thinking became known as “Pure Strategy Nash Equilibria*
As you can see, any individual seeking to create a strategy in a game will need to explore where a Pure Strategy Nash Equilibria fits in the process. To clarify this concept let us say that among game thinkers Nash equilibrium* is the name applied to a set of strategies which represents mutual best responses when compared to other available strategies.
Assuming that in a specific scenario (game) the other players will make what seems to them to be rational choices one might say that “every player is playing his or her part of a Nash equilibrium, and no player will have an incentive to unilaterally change his or her strategy.” In those games where players choose a single strategy without randomizing* (this is known by game theory experts as a pure strategy*) a game can have any number of Nash equilibria.
Another, simple explanation of Nash Equilibrium is the idea that if most players in a strategic game think logically or at least rationally then the optimal outcome of any game would be one where no player has an incentive to deviate from his or her chosen strategy after considering an opponent’s choice. Overall, an individual can receive no incremental benefit from changing actions, assuming other players remain constant in their strategies.
I have a personal interest in Win/Win games, the type of games explained by Nash, and though I am skilled and tend to succeed in win/lose scenarios I always tell my students that there are five fundamental techniques to win a game and do so without it being at the expense of others.
- Get essential information
- Gather influence
- Increase your income, power, and influence
- Reduce your expenses.
- Be mindful and present in the moment
- Act compassionately and with a generous heart
Gain wisdom and whenever possible make those choices that not only serve your own interests but which serve the interests of others.
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If you have an interest in having a basic understanding of Applied Game Theory (and you need to) here is an interview I did with James Selman, a pioneer and innovator in Leadership research.
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