Game Theory: Should You Push the Button?

From the lecture series: Games People Play—Game Theory in Life, Business, and Beyond

By Scott P. Stevens, Ph.D, James Madison University

Wanna play a game? It’s an easy game. All you have to do is decide whether or not to push a button. But either way, you must face the consequences.

Man with two hands about to press the button for answering a quiz question
Would you push the button? (Image: Olivier Le Moal/Shutterstock)

At the beginning of this game, you receive $100 and a button. Imagine that 100 viewers in 100 rooms across the country are reading this and that each has been given $100 and a button, just like you. In a moment, you will be asked to decide whether to push your button. That’s the only decision that you’ll have to make, and in doing so, you’ll be deciding upon a strategy.

In every game, every player has a strategy. A rational player will try to adopt the strategy that will maximize the expected payoff given what they know or think they know about the other players in the game. 

In every game, every player has a strategy. If you’re a rational player, you’re going to try to adopt the strategy that will maximize your expected payoff given what you know—or think you know—about the other players in the game. But you don’t know enough yet to know whether to push. What does it do? Pushing this button has two effects: one that affects you and one that affects everybody else. If nobody’s actions affected anyone else, it wouldn’t be a game because games are interactive.

This is a transcript from the video series Games People Play: Game Theory in Life, Business, and Beyond. Watch it now, on Wondrium.

When you push your button, the first thing it does is to take $2 away from every other player, and just like that, everyone else is down to $98. You still have your $100. It sounds vicious on your part, but other people may press their buttons, too, and every time they do, you lose $2 along with everybody else. If 60 other people pushed their buttons, you’re going to lose 2 × 60, or $120. Given that you only $100 to start with, you’re going to end up $20 in debt. You’ll have to pay up, except that there’s a way out of this for you.

Learn more about how “Games” apply to all aspects of life

Making Assumptions

Pressing your button has two effects and the second one targets you. If other people press their buttons and cause you damage, pushing your button will cut that damage in half. A moment ago, I said that if 60 people push, you lose $120, but if 60 other people push and you do, too, then you only lose $60; you’re still $40 to the good. You’ve done $2 damage to everybody else, but you’ve saved yourself $60. Are you going to push?

You probably made some reasonable assumptions about this game: You’ve assumed that everybody else’s button works the same way that yours does. It does because this game is symmetric; everyone is in the same boat. Also, you’ve probably assumed that everybody else has the same information that you do, meaning that the structure of the game is common knowledge.

But being common knowledge means more than that. It’s not just that everyone knows the rules of the game. Everyone knows the same information that you do.

Think carefully now and decide what you’re going to do: push or not push.

Learn more about rationality and common sense

Five Lines of Reasoning

Yes or no dilemma concept
To push the button or not to push the button? (Image: ltummy/Shutterstock)

You’re probably considering several different lines of thought right now. One line of reasoning is this: We all know how the game works. If nobody pushes the button, everybody gets $100. You might not even be concerned about being a nice person, but you don’t have to be. We can all get $100. You’d be crazy to push. That’s a good argument.

A hundred people. Some of them are going to push. No matter what the other people do, you’re at least as well off pushing as not pushing.

The second line of argument, perhaps the even more compelling one, is this: A hundred people. Some of them are going to push. No matter what the other people do, you’re at least as well off pushing as not pushing. If you don’t push, you could end up $100 in debt. If you push, at least you end up breaking even. You think you’re a good person, and if you’re thinking about pushing, you can imagine what the other people will do. You have to push in self-defense.

Here’s the third line: You won’t push the button, because it’s the right thing to do in a moral sense. You could lose up to $100 and go into debt, but it’s worth it for the sake of your ethics.

Or you may decide: $100; it’s not that much money. It would be too much fun to just stir things up and see what happens. Push the button. Or you may have a competitive streak, and you know that if you don’t push, everybody who does will end up ahead of you. Maybe you don’t have much of a taste for being a chump. Of these five lines of reasoning, it’s interesting to know which, if any, actually are rational.

Okay, it’s time to decide. I wish that I could tally the votes as they come in real-time, but of course, I can’t. What I can tell you after you make your choice are the results of similar games that I’ve played with other people. Make your choice and state it out loud; keep yourself honest. Push or don’t push.

With groups of strangers who have no training in game theory, generally somewhere between 30 percent and 70 percent of the people push the button. That’s a pretty wide range, but if you take the average, you get 50 percent.

If you didn’t push, that means that you’re now broke. If you pushed, you still have $50.

Learn more about how insisting you lose a competition can be a winning strategy

More than Just a Game

This might not make that much of an impact on you; after all, this was just a game of pretend. But the game is real; it’s not pretending. We’re not talking about child’s play here. We defined a set of possible moves by which players interacted with each other, they had common knowledge of the structure of the game, and they made rational decisions about strategies that led to their best-expected payoff. These components—players, strategies, payoffs, and common knowledge—are what makes a game a game in the game-theoretic sense. If you change the context of this game by replacing the players with countries and by changing the push of the button to being willing to engage in military conflict, then we have something much more than just a diversion.

The variety of responses that we’ve seen in this game—between 30 percent and 70 percent pushing—show that one of two things must be the case: Either the theory of game theory isn’t sufficiently common knowledge that people are comfortable choosing rightly, or maybe this game is an inherently dangerous one. Maybe we need to find a way to keep pushing the button from being so tempting an option because if 30 to 70 percent of the people in the nuclear version of this game decide to press the button, we’re all in for a very bad time.

The name “game theory” may be an unfortunate one. A more descriptive name would be “strategic interaction decision making.” Game theory sounds like child’s play, and it’s not.

Learn more about how to determine if a set of strategies is optimal

Common Questions About Game Theory

Q: Is Game Theory valuable in life?

Game Theory can be useful in life, but it has limited relevance to practical application. It is great for planning and strategy, but it largely only works when the players are acting in a prescribed rationality that is predicated on them going for the largest payday. In reality, there are many more factors at work. Thus, game theory is a good skeleton to hang deeper plans on, but not the complete picture.

Q: Is Game Theory used in any discipline or field of study?

Game Theory is used in many disciplines including military strategy, business strategy, economics, and diplomacy. Academic fields of study that employ game theory are computer science, psychology, sociology, and political science.

Q: Who created Game Theory?

Mathematician Lloyd S. Shapley is the creator and father of Game Theory.

Q: What is the meaning of Prisoner’s Dilemma in Game Theory?

The Prisoner’s Dilemma was created in 1952. It states that two individuals who are imprisoned and both completely rational actors will not cooperate, even if it is in their best interest.
In the example, both prisoners are in solitary confinement and may not communicate. There is not enough evidence to get them on the major charge but enough to get each on minor charges. They are given a deal to either testify and betray each other or remain silent and cooperate with one another. Betraying each other gets them both two years. If one betrays the other but the other stays silent, the one who stays silent gets three years while the snitch goes free. If both remain silent, they’ll both only serve a year.
The idea is that both will betray each other because of the purely rational gain of freedom rather than cooperate even though this dual betrayal ends in a worse outcome. That is the point: that cooperative behavior is not the usual outcome when the actors are purely rational.

This article was updated on May 26, 2020

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