Created by: Michelle Di Ionno, Quantitative Reasoning Fellow, Economics department Edited by: Ivan Levcovitz, Quantitative Reasoning Fellow, Economics department

**Learning Objectives: **

Students will be able to convert information into a mathematical diagram. They will also make/communicate judgments and draw appropriate conclusions based on the quantitative analysis of data.

**Key Terms:**

*Game theory** *– The analysis of strategies for dealing with competitive situations where the outcome of a participant’s choice of action depends critically on the actions of other participants.

*Social dilemma* – A situation in which an individual profits from selfishness unless everyone chooses the selfish alternative, in which case the whole group loses.

**Scenario**:

There are two suspects arrested for a crime: Henry and Dave. They are locked away in separate rooms, with no means of communicating with one another. The police interrogating the suspects offer the same deal to Henry and Dave.

The possibilities available to Henry is as follows:

- 1. Henry confesses and implicates his friend Dave. Henry’s sentence will be either:
- 5 years in jail, if Dave also confesses independently (Dave’s sentence will also be 5 years)
- 0 years in jail on a plea, if Dave does not confess (but in this case Dave will get 20 years)

- 2. If Henry holds out and does not confess or implicate Dave his sentence will be either:
- 1 year in jail on a reduced charge, provided Dave holds out as well (thus no confession from either)
- 20 years in jail, if Dave confesses and betrays Henry

The same possibilities apply to Dave as well.

1. Define the key terms for the class.

2. Explain the scenario of the prisoner’s dilemma.

3. Give the class 5 minutes to brainstorm a matrix for the prisoner’s dilemma.

4. Show the correct matrix to students:

(Example matrix below)

Graphic adapted from investopedia.com

5. Discuss the following:

- What are the implications of the prisoner’s dilemma?
*If one of the prisoners betrays the other, he may get a reduced sentence, but only if his friend does not also confess. This situation is risky for both prisoners. If both of them decide to betray each other, both of them will go to prison for five years. Only if both of them are certain that the other one will not confess, can they minimize their losses by not confessing at all.**The prisoner cannot make the best decision for himself without knowing what the other prisoner will do and they are unable to communicate with each other.*

- What do you think is the right choice for the prisoners to make? What would you do if you were one of the prisoners.
*Human actions are based on two factors: emotional motivators and rationality.**Math is mainly rational, but does not use emotionality.**It is possible that all humans will only act in their own self-interest.**What outcome does acting rationally or in one’s self-interest lead to?**When Henry is making a rational decision, he needs to think about what Dave may choose.**If Dave does not confess, Henry’s best choice is to confess (confessing = 0 years; not confessing = 1 year)**If Dave does confess, Henry’s best choice is, again, to confess (confessing = 5 years; not confessing = 20 years)**Therefore, the rational choice for both prisoners is to confess.*

*It is in both of their self-interest to confess, as confessing leads to the better outcome when their friend’s decision is unknown. This leads them to each spend five years in jail.**Obviously a better outcome would be if they both held out and only had to spend one year in jail each. However, without knowing the other’s decision, holding out is extremely risk**y**and would likely not be chosen by either party.*

6*. *Ask students to brainstorm different scenarios where game theory applies as well.

**Download: **

Word Document: Prisoner’s Dilemma

Powerpoint: Prisoner’s Dilemma

**Sources**:

http://www.rationality.net/prison_dilem.htm