Oligopoly

- Is the activity appropriate for principles courses, intermediate courses, or selective elective courses?
o Principles
- What prior student knowledge is required?
o Oligopoly, payoff matrix, strategies, Nash equilibrium
- Are there class size limitations?
o No
- How much time is needed for the activity? Does it extend across more than one class period?
o About 50 minutes
- Is this activity connected to another TBL activity? If so, please provide a link to that activity. For example, is this activity part of a group of activities within a single TBL module?
o This activity can be used on its own, though it is part of a series of activities in the same module.

Overview

Stylized version of the 1990's decision by Airbus and Boeing, when both companies were researching the feasibility of a very large passenger aircraft. Uses game theory (strategies, stylized payoffs, Nash equilibria).

Expected Student Learning Outcomes

- Contrast collusion and competition
- Analyze oligopoly situations using game theory
- Identify players, strategies, and payoffs in a strategic economic situation
- Calculate the Nash equilibria in a one-shot game

Information Given to Students

Oligopoly (Microsoft Word 2007 (.docx) 18kB Oct1 18)

The purpose of this application is to introduce students to analyzing a type of strategic interaction between firms (duopolists) using game theory for the first time. Before tackling this application, students have read the chapters on oligopoly and game theory. In the OpenStax textbook, game theory is not explored in depth, so before this application students have only seen a 2-player, 2-strategy payoff matrix, discussing the Nash equilibrium only in a prisoner-dilemma-like setting. This application is the first that allows them to practice those concepts and tools.

Part 1 does not cause any problem. Before students create the payoff matrix, it is useful to tell them what player goes in the rows, and remind them of the convention about the order of payoffs, so all teams create a similar payoff matrix (as opposed to having the payoffs or players switched). Comparing answers across teams at this point allows everyone to start from a common payoff matrix.

Part 2 usually is pretty straightforward, and you may want to consider having teams solving parts 2 and 3.

Part 3 is where the fun begins. This is the first time teams are trying to find a Nash equilibrium. Common mistakes include expressing the equilibrium in terms of payoffs, instead of strategies, or insisting that if both firms would be better off by colluding, then they would both switch, without realizing that the Nash equilibrium requires each player to consider her strategies and payoffs while keeping the other player's strategy constant.

Part 4 encourages students to transform the payoff matrix in such a way that both firms would find themselves colluding in the new Nash equillibrium. The discussion question aims at having students think outside of the mini-universe of the two firms, and what would be the impact on consumers and others. This is a good time to talk about antitrust legislation and its purpose (for example, the contract proposed in part 4 would be illegal in the U.S.).

The game was presented as a one-shot simultaneous game. After parts 3 and 4, it would be useful to talk about what would happen in a repeated game, when Boeing and Airbus keep meeting each other, and whether the players might be able to sustain a collusive equilibrium, even in the absence of an explicit contract (that is, without modifying the initial payoff matrix).

Note that in my class each team has a small whiteboard (sometimes called a huddleboard) to respond to most questions, and they share their results by raising their whiteboards simultaneously (the whiteboards/huddleboards are small and light enough that they can be raised by one person, and they are big enough that everyone can observe the results of all other teams).

Observation and discussion of student answers. Module ends in a capstone test. Final exam also tests these learning outcomes.