Problem

Maggie and Lou are found at a crime scene. Given the physical evidence, they’re each looking at about one year in prison. However, the cops want more than that. They take Maggie and Lou to separate holding cells and present them each with a dilemma: to either testify against the other or remain silent. If one of them chooses to testify and the other remains silent, then the testifier will be given full immunity while their cohort will be sentenced to 6 years in prison. If both parties blab, they’ll each be charged with a prison time of 3 years. Of course, they could both keep quiet and get off with only one year each. Both suspects are told that their alleged partner is presented with the same deal. A little while later the police have testimonies from both Maggie and Lou – why?

Here’s Why

This scenario is known as the prisoner’s dilemma, and it’s a classic example of game theory. By modeling potential interactions between people, we can understand why rational beings sometimes make choices that seem counter-intuitive. 

The Prisoner’s Dilemma

Game theory is the model framework for understanding strategic decision making among individuals, or players. Prisoner’s dilemma is an example of noncooperative game theory that demonstrates why two rational individuals would refuse to work together even if it might be in their better interest to do so.

How It Works

Game theory provides tools to study a vast amount of human interactions, or games. An individual’s choices in these games affect another’s gains or losses. Two big categories of game theory are cooperative and noncooperative. In cooperative game theory, it’s in players’ best interests to form teams, and the bonds between teammates can be trusted. Together they work toward a shared goal. Noncooperative games are the exact opposite: they’re competitive. Everyone is working to their own benefit. To fully understand the difference, let’s examine the competitive prisoner’s dilemma.

Take Lou’s perspective. Maggie isn’t your sister or girlfriend or even friend. You have no reason to believe she isn’t going to take that attractive immunity deal. If she talks, it’s in your best interest to talk too. Even if she stays silent, talking is still your best option – you’ll get off with no jail time! Since you can’t control Maggie’s behavior, testifying against her is the smartest choice you can make. 

The same logic applies to Maggie’s perspective. Therefore, both parties will end up testifying against the other. This is because their situation isn’t conducive for cooperative play. Maggie and Lou stand to gain from betraying the other.

Using It

Game theories are used daily in so many fields. Companies use them to determine sale prices. Philosophers use game theory to create and debate moral dilemmas. They’ve even been employed in the political sphere: game theories were applied to the Cuban missile crisis in 1962. The event has often been compared to a high-stakes game of chicken, but it can also be modeled with a simple chart, not unlike those used to explain the prisoner’s dilemma.

Each player then had two possible choices to make. For the US, it was to make a “surgical” air strike, wiping out the installed missiles by force, or to de-escalate the conflict by lifting its naval blockade. The Soviet Union meanwhile could either maintain their missiles or withdraw their missiles from Cuba in a bid for peace. Combined, these moves could lead to one of four main outcomes: US victory, Soviet victory, compromise, or mutually assured destruction in the form of a nuclear war. 

Neither party wants to lose the game. They want to win. Following the logic of the prisoner’s dilemma, that meant that, even though it’s objectively the worst option, both parties came dangerously close to starting a nuclear war no one would survive. So why didn’t they? Simple: they changed the rules of the game.

A prisoner’s dilemma mainly works because the two parties can’t communicate. If they’re allowed to talk, the game stops being competitive, so the chances of backstabbing decreases dramatically. Rational individuals are willing to compromise if it ensures that they won’t lose. With a loss situation as big as mutually assured destruction, US and Soviet leaders were willing to compromise once they actually talked to each other.

Whether it’s in political science, biology, computer science, or economics, game theories are used to model human behavior and help determine what’s the smartest or the fairest way to approach a problem.

    Learn More

    1. Basar, Tamer and Geert Jan Olsder. Dynamic Noncooperative Game Theory: Second Edition. Society for Industrial and Applied Mathematics, 1999.
    2. Osborner, Martin J. and Ariel Rubinstein. A Course in Game Theory. The MIT Press, 1994. ISBN: 0-262-15041-7.
    3. Rabin, Matthew. “Incorporating Fairness into Game Theory and Economics.” The American Economic Review, vol 83, no 5, Dec 1993, pp 1281-1302.
    4. Roughgarden, Tim. “Algorithmic game theory.” Communications of the ACM, vol 53, issue 7, July 2010. Doi: 10.1145/1785414.1785439.
    5. Zagare, Frank C. “A Game-Theoretic History of the Cuban Missile Crisis.” Economies, volume 2, issue 1, 2014, pp 20-44. DOI: 10.3390/economies2010020

    Think Further

    1. What’s the last time you used or saw game theory used in your life?
    2. What are some real life examples of cooperative games?
    3. Do you think the prisoner’s dilemma is effective at getting suspects to testify, allowing for an indictment to be reached? Why or why not?

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