Quick Class 13: GAME THEORY – B2/C1

1)  Match the words and definitions*

2)  Discuss the following:

• Imagine this situation: You and your partner are criminals who have been just arrested by the police. Both of you have committed the crime together and the police have all the information, so the two of you are definitely going to jail. But then the police propose a deal to both of you. If one of you confesses to the crime and the other doesn’t, the one who confesses is set free immediately while the other one spends 10 years in jail. If neither of you confess, then both of you will spend two years in jail. And if you both confess, you will both spend five years in jail. You should keep in mind that have only recently met your partner and you have no real reason to trust him. Your partner, of course, feels the same way about you. When the police take you different rooms to get your testimonies, will you confess or keep quiet?

3)  Listen to the audio and answer the following questions:

• What is most plausible result of the Prisoner’s Dilemma?
• In what ways is game theory applied to real situations?

4) Now read the transcript below and check your answers:

Imagine this situation: You and your partner are criminals who have been just arrested by the police. Both of you have committed the crime together and the police have all the information, so the two of you are definitely going to jail. But then the police propose a deal to both of you. If one of you confesses to the crime and the other doesn’t, the one who confesses is set free immediately while the other one spends 10 years in jail. If there’s no confession from anyone, then both of you will spend two years in jail. And if you both confess, you will both spend five years in jail. You should keep in mind that you have only recently met your partner and you have no real reason to trust him. Your partner, of course, feels the same way about you. When the police take you different rooms to get your testimonies, will you confess or keep quiet?

This is what is known as the Prisoner’s Dilemma and it is commonly used to explain a mathematical theory of social interaction called Game Theory. Game theory was first conceptualized by the American mathematician John Nash, who was made famous by the movie A Beautiful Mind, where he is played by Russel Crowe. In very simple terms, Game Theory analyzes what is the most plausible outcome of an interaction between two or more participants in a state of competition or cooperation in a game-like scenario.

In the case of the Prisoner’s Dilemma, Game Theory says that the most plausible outcome would be of both prisoners choosing to confess and then spend 5 years in prison each. And that is because they won’t trust each other to keep quiet and will probably prefer to pursue the best result for them, namely trying to spend no time at all behind bars hoping the other one will refuse to confess.

All this is made immensely relevant once we consider that Game Theory is applied in a similar way to decision-making processes in other game-like scenarios, such as politics and business. In politics, for example, Game Theory can be used to determine the possible guarantees of cooperation among heads of state negotiating the terms of a pact or a treaty, or similar deals…

And in business, Game Theory plays an important part in determining whether to set up shop close or far away from your competitor, the prices of different products and other elements related to competition. For instance, if two ice cream parlors are located on the opposite extremes of a beach, both getting 50% of the available clients, one of them may think it’s a good idea to move closer to the center of the beach, which would give it 75% of clients against the 25% of the one that remained on one of the extremes.

But then this other ice-cream parlor decides to also move closer to the center of the beach to even things out and, by doing that, return to its original economic situation of getting 50% of all clients by locating itself right next to its competitor. We see this happening every day in any big city. And the same goes for the prices. If one ice-cream parlor lowers the price to sell more ice-cream, the other one may be forced to do the same.

Of course, the two competitors may simply agree to increase prices evenly so both of them can make more money, but this could lead to a third ice-cream parlor setting up shop in the area with lower prices, which would force its competitors to change their strategy to continue in the game.

So that is Game Theory in a nutshell. And if you thought mathematics couldn’t be fun, you could not be more wrong.

*Answers to exercise 2: a-3, b-5, c-6, d-1, e-2, f-4