# Game theory: externalities, the prisoner's dilemma and Nash equilibrium as seen in South Park

## Summary

## Context for Use

Class size: 50 and under

Prior knowledge: students should be familiar with how to represent strategies and outcomes using a game theory matrix as well as the concepts of prisoner's dilemma and Nash equilibrium

Time: About 35 minutes: 5 minutes to read article, 15 minutes to work in groups to create game, 15 minutes to discuss

## Overview

After viewing a brief segment of a South Park episode, students create a game theory matrix and apply the concepts of the Prisoner's Dilemma and Nash Equilibrium.

## Expected Student Learning Outcomes

Students create a game theory matrix and apply the concepts of the Prisoner's Dilemma and Nash Equilibrium.

## Information Given to Students

Economics is everywhere – even in South Park. If you're not familiar, South Park is an animated sitcom for adults featuring the adventures of four grade-school boys in the town of South Park, Colorado. In season 13, episode 14, the boys go to Pi Pi's Water Park. Everybody is peeing in the pool and the pee concentration ends up being so high that it causes a flood that destroys the place. You can watch a clip of the episode here:

http://www.criticalcommons.org/Members/economicstube/clips/pee_in_pool.wmv

**Part One**

1. Using two South Park characters, create a pay-off matrix to represent the decisions faced by each of the two chosen characters.

2. Determine each player's dominant strategy (if one exists).

3. Identify the outcome of the game.

4. Be prepared to discuss the following questions:

a. Are the characters in a Prisoner's dilemma? Why or why not?

b. Is the outcome of this "game" a Nash equilibrium? Why or why not?

c. What are some additional examples of firms or countries being faced with a prisoner's dilemma?

**Part Two**

1. Describe a "real-world" example of a prisoner's dilemma with which you may have direct experience.

Reporting will be done in gallery walk format.

## Teaching Notes and Tips

Most students are familiar with the Comedy Central series South Park. It is a very crude, animated sitcom that has been on the air since 1997. While this show can be offensive, it is popular and often displays, in the real world, the economic concepts students are studying in class.

In a few minutes, students can take concepts they already understand (acting in own self-interest, externalities) and apply game theory constructs. It is probably pretty obvious why each child might choose to pee in the pool (less costly in terms of time, etc.) and even more obvious what will happen if everyone chooses to act in their own self-interest.

Since the instructions about the game theory matrix are quite vague, there may be a variety of representations which can lead to good discussion.

Prefatory remarks:

Economics happens. Daily. It happens on Wall Street and on Main Street; on the trading floor and in the grocery store. It is like a word you hear for the very first time and then it pops up over and over – once you're exposed to economic concepts they seem to appear everywhere. It even shows up in South Park. You already know about people acting in their own self-interest (that was Adam Smith's invisible hand), now you will apply that to a South Park clip and show how the characters in the clip might be facing a prisoner's dilemma.

Discussion questions:

What is meant by the concept of a prisoner's dilemma?

In looking at your game theory pay-off matrix, are your characters trapped in a prisoner's dilemma? Why or why not?

Peeing in the pool is most definitely a negative externality. What causes externalities? What are some of the ways to solve them? Would these solutions work in a place like a public pool?

**What are some of the ways that the prisoner's dilemma can be "solved" or avoided?**

Closing remarks:

Top 3 takeaways

1. Everyone acting in their own self-interest (the guiding principle of market economies) does NOT always make everyone better off. It can lead to negative externalities and unintended consequences.

2. A prisoner's dilemma is when each player, acting in their own self-interest ends up leaving both players worse off. Examples of prisoner's dilemmas abound.

3. Changing incentives to promote cooperation among players (e.g., tit-for-tat) is a way to avoid or escape the prisoner's dilemma in the long run.

## Assessment

## References and Resources

http://www.criticalcommons.org/Members/economicstube/clips/pee_in_pool.wmv