Tragedy of the commons game

This activity is suitable for use in introductory microeconomics classes or in environmental economics classes. The activity could be included in a unit on game theory or in a unit on open-access resources. Students should have been exposed to the basics of game theory analysis via reading assignments and RAP quizzes. The activity would work in classes of any size. Students need not have studied open-access resource issues before doing the exercise, though in that case, the term "open-access" would require definition in instructor remarks preceding the exercise. The exercise, including prefatory remarks, student work, debriefing, and instructor summary comments should take approximately 40 minutes of class time.

Overview

This application calls on student teams to depict a tragedy of the commons game in strategic form, identify the Nash equilibrium outcome, and consider policies that might improve on an open-access management regime for a potentially renewable natural resource. Rather than reporting by means of an ABCDE single choice, student teams post their completed game matrix with the Nash equilibrium highlighted along with a sentence summarizing their policy recommendation.

Expected Student Learning Outcomes

Upon successful completion of this learning activity, students will be able to ...
* Construct the strategic form of a game from information on players, strategies, and payoffs.
* Identify Nash equilibria in games.
* Explain the market failure that results when potentially renewable resources are regulated in a way that allows open access to the resource.
* Evaluate policy measures to address market failure in the area of common-pool (aka open-access) resources based on benefits and costs of the alternative policies.

Information Given to Students

Tragedy of the commons game

1. Model the tragedy of the commons as a game played among Farmer Anita and all other farmers who share a pasture with limited capacity.
2. Each farmer has strategies to graze one milk cow or two milk cows. (Hint: model all other farmers as one player.)
3. Payoffs range from 1 (worst) to 4 (best).
4. Indicate the Nash equilibrium of your game.
5. What policy intervention would improve the situation? (Summarize your policy recommendation in a sentence displayed with your game on an 8.5" x 11" sheet of paper.)

Gallery walk reporting!

Prefatory remarks should be kept to a minimum. Defining open-access resources briefly for classes in which students have merely studied the basics of game theory beforehand is all that is necessary.
There are many ways to pick reporters in gallery walk exercises. The best way depends in part on the distribution of answers. I'd have two reporting phases: one for the game and Nash equilibrium depiction, another for policy measure. If there are just a few right answers, I'd call one reporter from teams that got the wrong answers in each unique way. (As always, be sure to avoid giving too much away as you step in to help teams that might be stuck during the work phase.) Then call on a reporter from one of the teams that produced the correct answer. Even if all teams have the correct depiction of the game and Nash equilibrium, I call on one or two reporters to come to the doc cam to explain the diagram to the class. It is essential to make sure that every student in the team be liable for the report until after the exercise is completed. The only way students in my classes lose points for the application exercises is if a student reporter ever says "I don't know." or "We just guessed." or "My team mate can explain better than I can." So the student reports are vital.
There ought to be a wide distribution of policy measures suggested. Limiting grazing to one cow. Tradable permits. Grazing fees. Let students argue it out. The policy discussion is more rich for a class studying the tragedy of the commons than it is for a class using this exercise to learn game theory basics.

End-of-module quizzes, exams, and/or final can include similar questions to assess student mastery.