Originally published July 2021. Updated April 2026.
I could explain game theory to you, but film director Rob Reiner (RIP) did it best. In his 1987 epic fairytale adventure, The Princess Bride, actors Wallace Shawn and Cary Elwes demonstrate classic game theory as Vizzini and the Man in Black. Vizzini and The Man in Black engage in a “battle of wits” over two wine goblets—one of which has been poisoned.
Vizzini’s logic spirals from the outset. “A clever man would put the poison in his own goblet because he would know that only a great fool would reach for what he was given. I am not a great fool, so I can clearly not choose the wine in front of you. But you must have known that I was not a great fool. You would have counted on it, so I can clearly not choose the wine in front of me.”
This “divining” goes on for several minutes, and it’s a perfect introduction to game theory: the study of interactive decision making. This is strategic interdependence, where the outcome for each participant depends entirely on the actions of the others. When choosing a strategy in game theory, you’re forced to consider the choices of your opponents while knowing that they, in turn, are taking your choices into account.
UNDERSTANDING GAME THEORY
At the end of the encounter, we learn that Vizzini and The Man in Black weren’t actually playing the same game. Vizzini believed he was playing a game that he could win or lose, but he was wrong. The Man in Black secretly poisoned both cups because, as we later learn, he is immune. He held “asymmetric information,” in this case, about a fundamental condition of the environment, which his opponent didn’t have. This kind of gambit brings us to a level of game theory beyond my mathematical capabilities, so let’s go back to the beginning.
Game theory is a highly structured branch of applied mathematics that can be applied to any number of things—economics, politics, or even biology. It began in the mid-20th century with the work of John von Neumann and Oskar Morgenstern, who mostly studied zero-sum games. In a zero-sum game, one player’s gain is exactly equal to the other player’s loss; the interests of the players are strictly opposed.
Tic-tac-toe and chess are examples of zero-sum games. They’re both games of perfect information, meaning that each player can see the board and knows everything that is happening in the game at all times. Compare that to a game like poker, which is also a zero-sum game but with one important distinction. Unlike chess, poker is a game of imperfect information. Because poker players can’t see their opponents’ cards, each player must make decisions based on probabilities and hidden variables.
In the 1940s and 1950s, mathematicians like John Nash began applying game theory to more realistic scenarios in which participants might have a mix of common and competing interests and in which there could be any number of players. The quintessential example of game theory, as framed at that time, is still used today to explain how it works—the prisoner’s dilemma.
Imagine that two people are arrested for a burglary that they committed together. The police put them in separate rooms and offer each a deal.
If both stay silent, both prisoners will get one year in jail.
If one rats and the other stays silent, the “rat” goes free, but the other prisoner gets a 20-year sentence.
If they both rat, they both get five years.
Game theory gives us a way to figure out the best strategy—let’s consider this from prisoner A’s perspective. At first glance, it might look like prisoner A should stay silent, because if his partner also stays silent, they each only get a year in the slammer. But remember that game theory requires you to consider what the other player is thinking about. If player B thinks player A is going to stay silent, he could be tempted to rat him out and walk free.
This is where we turn to math. If player A stays silent, he’ll either get one year or 20, for an average sentence of 10.5 years. If he rats his partner out, he gets no years or 5, for an average of 2.5. Mathematically, it makes the most sense for prisoner A to rat on his partner.
In game theory, this is called a “dominant strategy.” Regardless of what his partner in crime does, prisoner A is better off betraying him. If both players make this move, they’ll each end up with a five-year sentence. While this is a worse outcome for the group, it’s a logical way to minimize individual risk.
HOW IS GAME THEORY USED?
The prisoner’s dilemma is a great introduction into how game theory works for us non-mathematicians, but it doesn’t take long for the math behind game theory to get very complex. Imagine what happens if a game is played more than once. Most “games” in real life don’t involve drinking poison from a cup—most of the time, we’ll live on to play another round.
This introduces the concept of iteration. What happens when you consider that your opponent will look at what you did in round one and use that in determining their strategy for round two? What happens when there are infinite rounds? What happens when players have both common and opposing interests? What happens when there are a dozen players instead of two?
This is where game theory can become a vital tool for helping people, teams, and entire nations develop strategies in any number of scenarios. Consider two nations with a boundary dispute. Both want a specific parcel of land (opposing interests), but they also want to avoid a costly war (common interest).
To look at a less high-stakes example, consider a gas company determining what price to set for its fuel. If they keep the price high, they’ll make more money, but only until a competitor sets a lower price and they start losing business. But if they lower their price, will the competition follow suit in a race to the bottom until nobody is making a profit?
We even see game theory applied in auction markets to help determine how bidders will act and predict probable outcomes. Game theory must consider the value of each item being auctioned. It must also consider how much each individual may desire an item. But is there an equation that can take into account bidders being slightly tipsy? And how such intoxication makes a bidder absolutely sure that she needs a large metal frog playing the saxophone as a house decoration? I’m asking for a friend.
Which brings us to the most important question: how do we win when the rules keep changing?
YOU ASSUMED WHAT??
While game theory is a powerful tool for mapping out strategy in all kinds of situations, it’s based on the substantial premise that every player is acting rationally. You don’t need to have dropped a few hundred on a large metal frog sculpture (because, ha-ha, who does that?!) to know that humans are not entirely rational creatures.
We’ve mentioned the researchers Daniel Kahneman and Amos Tversky before. In the 1970s, they introduced behavioral economics, or the idea that humans don’t behave rationally when making economic decisions. Mathematically, a 95 percent chance of survival and a 5 percent chance of dying are identical—they’re two different ways of looking at the same statistic—but our human brains don’t interpret it that way. If people were rational, the lottery wouldn’t be a thing.
Game theory gives us an excellent framework for helping us make decisions by “thinking about what someone else is thinking about.” It prompts us to ponder all of the different possibilities in a given situation, and to dig deeper into an individual’s motivations. Sounds useful for sales professionals, doesn’t it? It is! But you’ll have to wait until next week to learn more about that.
PROOF THAT WE AREN’T RATIONAL
Game theory assumes that all players act rationally, but the players are human, so we know that’s not quite true. One thing humans are notoriously bad at is estimating risk for certain situations and behaviors. Case in point: 34 percent of Americans are terrified of sharks.
Statistically speaking, the odds of getting attacked by a shark are incredibly low. How low? Here are some things that should scare you more than sharks.
- Sunstroke—Your chances of dying from sunstroke (which you’ll get when you refuse to go into the water due to your unreasonable fear of sharks) are one in 3,740.
- Cows—You’re at least 4x more likely to get trampled to death by a cow than eaten by a shark.
- Selfies—51 deaths a year happen while taking a selfie. Only 10 a year for sharks.
- Hot stuff—Kills one in 45,318.
- Sharp stuff—Kills one in 20,599.
- Hot, sharp stuff—I have no idea, but I think you get my point.
You are much more likely to be attacked by a shark than you are to win the lottery, but that’s more of an indictment of lotteries than it is of sharks.
Do you want to dig into how game theory can help you hone your sales skills? Contact us at mastery@maestrogroup.co.