# Game Theory Simulation Exercise: Pricing Prisoner's Dilemma

## Summary

Student teams act as firms and make strategic pricing decisions. Each firms' profits depend on all of the teams' decisions.

## Context for Use

This activity was designed for principles courses that cover basic game theory, but could also be used in intermediate micro or game theory classes. It will take 50-75 minutes. The activity starts with a readiness-assessment quiz, which is followed by the game theory simulation.

## Overview

This activity places student teams in a simple strategic market simulation. Each team has a binary choice - price low or high - and will earn profits based on both their and opposing teams' choices. The structure is a multiplayer prisoner's dilemma among the teams; the challenge to students is to find ways to profit through strategic interaction when direct collusion is expressly prohibited. Specifically, they are not allowed to talk with other teams and plot strategy. Rather, they can make public declarations of their choices and their response to other teams' choices. If they are creative they can use such declarations to signal threats / promises that may allow for some collusion among the teams. However, collusion is a challenging and instructors should expect the students to get frustrated with the pricing strategies of other teams.

## Expected Student Learning Outcomes

Students will apply game theory principles to their own choices in a pricing simulation. After the simulation they should be able to clearly elucidate how prisoner's dilemmas in pricing both are challenging to firms but can sometimes be overcome to the detriment of consumers.

## Information Given to Students

Student teams are given folders with the quiz and then the handout with instructions for the simulation.

Quiz - basic game theory (Microsoft Word 2007 (.docx) 20kB May14 18)
Application Exercise - Game Theory Simulation (Microsoft Word 2007 (.docx) 13kB May14 18)

## Teaching Notes and Tips

This activity includes both a readiness-assessment quiz and application exercises. The quiz is ten multiple choice questions on basic game theory that has been previously covered in both readings and class lectures or activities. The quiz is posted online for individual completion before class and then given to each team to take again in class along with immediate feedback scratch cards.
The application exercise puts student teams in a multiplayer prisoner's dilemma in the form of a pricing game. Each team will have a simple binary choice to price low or high. For each round, the instructor should indicate when choices must be made and all teams should then reveal their choices simultaneously by holding up a letter (assign "A" for high and "B" for low to use the normal TBL letters). The instructor notes how many teams priced low or high, announces the results, and then tells students to prepare for the next round.
The game is setup so that direct collusion is prohibited, but students can make declarations, which can be used to indicate strategies such as grim-trigger ("if any other team prices low, we will price low from this point forward") or tit-for tat. The game is repeated to allow for such strategies and the number of rounds, while finite, is left uncertain so that students cannot plan on when the final round will be.
The instructor can use the payoffs as a low-stakes grade or extra credit points to incentivize student engagement if desired (this may also result in high levels of frustration).
Once the simulation is ended, the instructor should lead a reflection / discussion on what was evident in the game. Was there collusion? Why or why not? Did the outcome resemble a competitive market outcome? Why did some firms do better and others worse? Instructors can also assign students a brief reflection as homework; this is often useful when the simulation gets intense and the extra time allows for reflection with a cooler head.

## Assessment

Quiz grades provide evidence of preparedness and general understanding. Exams using application type questions assess the students' ability to meet the learning goal for this activity