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Bertrand Competition and Collusion Module

  1. Module Overview and Objectives

    This 30-minute module can serve as an introduction to Bertrand Competition or to build intuition following a lecture on the Bertrand Paradox. This module has the following learning objectives:

    • Show students that a market for a homogenous good without capacity constraints leads to vigorous price competition and marginal-cost pricing in equilibrium (the Bertrand Paradox)
    • Communication and indefinite repetition facilitate collusion.
  2. The Module: A Brief Summary

    Each student acts as a firm engaged in a duopolistic Bertrand competition for selling course notes. Each pair of students interacts across five rounds of play. In each round, players must simultaneously decide on a price to charge for course notes in the current round. The firm that posted the lowest price receives all of the sales for that round.

    Each unit of course-notes costs $2 to produce (MC=$2). The market demand for course notes is given by Q(P)=100(362P)=3600200P. The Nash Equilibrium price in a Bertrand duopoly competition is P=MC=$2. At this price, the total market quantity is Q=3200 and is split evenly between the two firms, q1=q2=1600 . Each firm earns zero profit in equilibrium.

    The first game in this module is a baseline Bertrand game. In the second game chat and indefinite repetition are enabled to facilitate collusive arrangements. This should result in higher prices and lower consumer welfare.

    Module Procedures in Brief

    • Run the Open Session for Students Survey.
    • Have students login
    • [Minutes 0-4] Review Instructions, ideally by projecting video
    • [Minutes 4-8] Run Instruction Comprehension Survey
    • [Minutes 8-12] Run the Five-Round Game
    • [Minutes 12-14] Run the Relection Survey
    • [Minutes 14-19] Review Results
    • [Minutes 19-25] Run the Indefinitely Repeated Game with Chat
    • [Minutes 25-27] Review Results
    • [Minutes 27-30] Final Reflection Survey
    • [Variable] Open Discussion
    • [Variable] MobLab Experience Survey
      • At the end of the module please administer our MobLab Experience Survey. You can set the game duration to be 24 hours which allows students ample time to complete the survey outside of class.
  3. Detailed Procedures

    • [Before class] Log in to MobLab. Create a new playlist by clicking the "+" button next to "Playlists" in the top left of the Instructor Console.
      • Give your newly created playlist a name your students will find informative.
      • Add the module to your new playlist by clicking the "Add" button or dragging it over.
    • [Shortly before class] Run the Open Session for Students Survey. While this survey has no actual questions (only a waiting message), running it before class ensures that students logging into MobLab will be able to access this session (playlist) immediately.
      • With the Open Session for Students survey expanded, click Run Survey followed by Begin the Game.
    • [As students are entering] Have all students log into MobLab, either with the app on their mobile devices or in a browser (moblab.com).
    • [4 minutes] Review the instructions with students. Expand the first game and click Instructions. If your classroom has audio capabilities, we recommend clicking Video Instructions in the resulting popup.
    • [4 minutes] Run the Instruction Comprehension Survey.
      • You may need to finish the Open Session for Students survey before starting the Instruction Comprehension survey.
      • The survey consists of five questions related to the rules of the game and how payoffs are calculated:
        • Question 1: Rules Review (no answer)
        • Question 2: Marginal Cost Answer: $2 (Choice B)
        • Question 3: Pricing below marginal costAnswer: False (Choice B)
        • Question 4: Hypothetical profit calculation Answer: 0 (Choice A)
        • Question 5: Hypothetical profit calculation Answer: 1600 (Choice B)
      • Work through the questions with your students.
      • Ask if they have any questions.
    • [4 minutes] Run the Five-Round Game. Each round will last 45 seconds, each pair of students will proceed as fast as the slowest student.
      • After pressing Run Game and then Begin the Game! in the resulting popup, the game will start on student screens, and your screen will switch to the game monitor.
      • After approximately 25 seconds, click Add Robots (if the final group contains fewer than 2 students).
      • When the final market has finished the fifth round, click Finish to end the game.
    • [2 minutes] Run Reflection Survey
      • Discuss the premise of the question:
        • Describe the motivation behind the decisions you made in this game. First, recall your thought process when you set price in the first round. Second, explain how your price setting evolved across time.
      • Question 1: What price did you set in the first round? What factors did you consider when choosing what price to set in subsequent rounds?
      • If you award participation marks for MobLab performance, we recommend awarding full credit for any thoughtful response.
    • [5 minutes] Discuss Results
      • Click results.
      • You will see graphs for Market Prices Across Rounds and Prices Announced Across Rounds (typical results shown in Figures below)
      • Using the checkboxes in the legends for these two graphs, hide all of the lines.
      • Reveal the Monopolist Price. Explain that if firms were not engaged in competition and only thinking about what price maximized profit this would be the price chosen.
      • Reveal the Equilibrium Price. Explain that each firm has the incentive to undercut their competitor to sell to the whole market. But, pricing below $2 leads to losses.
      • Reveal the market prices. The box plot indicates the maximum, median, and minimum market price across all groups. Explain that in each round the market price for a group is the lowest price posted.
        • In Figure 1 below there are four total students playing and hence two different groups. The market price in one group was about $13, and the market price in another group is a little over $11. Hence, the median market price across the two groups is a little over $12.

        (Figure 1: Typical Market Price Results from Bertrand Competition. Click to expand)

      • Now turn to the Announced Prices
      • Reveal the Monopolist Price
      • Reveal the Equilibrium Price
      • Reveal the Announced Prices. Explain that the box plot indicates the maximum, median, and minimum posted prices across all groups. Posted prices are not necessarily the lowest prices within a group.
      • Explain that this graph shows that not only is one firm moving towards marginal cost pricing (which could have given the result from the first graph), but all firms are doing so.
        • In Figure 2, in the first round of this example, the highest posted price across both games was close to $18, and the lowest posted price was close to $12.

        (Figure 2: Typical Posted Price Results from Bertrand Competition. Click to expand)

      • Scroll down.
      • Click on Final Round Price to order price from lowest to highest.
      • Explain at this price (likely approximately $2) the final round efficiency is close to 100% (where 100% is the perfectly competitive result). With two firms in this homogenous product (no capacity constraint) market the welfare and efficiency of a perfectly competitive market are replicated. Students should be astounded!
      • If you wish to show students the posted price of each group, you can do so by using the final graph in the results section. To switch between groups, use the table above the graph.
      • If you are running short on time, we recommend that you skip showing the prices across time for each specific groups.

    • [6 minutes] Run the Indefinitely Repeated Game. After a minimum of five rounds each pair of students will have a 75% chance of proceeding to additional rounds in the game. If you are running short on time remember you can press Finish at any time to end the game.
      • Inform students that they will be re-matched with someone different
      • Inform students that the exact number of rounds in this game is unknown. It could be five rounds, ten rounds, or even twenty rounds.
      • Inform students that in this round, they can exchange messages with their competitor.
      • After pressing Run Game and then Begin the Game! in the resulting popup, the game will start on student screens, and your screen will switch to the game monitor.
      • After approximately 25 seconds, click Add Robots (if the final group contains fewer than 2 students).
    • [2 minutes] Discuss Results
      • Click results
      • Using the checkboxes in the legends for these two graphs, hide all of the lines.
      • Reveal the Equilibrium Price. Explain that competition led to marginal cost pricing in the first game.
      • Reveal the Market Prices. Explain how the market price and posted price is higher than in the previous game.
      • Reveal the Monopolist Price. Specifically, note that the median prices in the market should now be closer to the price that a monopolist would charge.
        • If you do not get the expected results of higher market prices, ask the class about why they chose to post low prices like the previous game.
      • Scroll down.
      • Click on Final Round Price to order from highest to lowest
        • Point out from the table that since collusion raises the market price, there is lower consumer surplus and higher producer surplus in the market.
        • Because the market outcome is closer to that of a monopoly, the market efficiency also decreases.
    • [3 minutes] Run Final Reflection Survey
      • Discuss the premise of the question
        • We have seen that collusive arrangements increase prices and decrease consumer welfare. What factors does this experiment suggest are important in facilitating collusion? Can you think of additional factors?
      • Question 1: What do you think are important factors for firms to have success in colluding to set higher prices?
      • If you award participation marks for MobLab performance, we recommend awarding full credit for any thoughtful response.
    • [Variable] Open Discussion
      • The open discussion can focus on communication that helps to coordinate prices at the monopoly price across time and indefinite reputation that increases the stream of future benefits from cooperating at an above equilibrium price.
  4. Notes

    • Playing this game after lecturing on Bertrand competition, the Bertrand Paradox, and collusion may be helpful as the game will build intuition for these lessons and also help improve the likelihood of convergence.
    • We recommend keeping group size at 2 to highlight that marginal cost pricing in Bertrand competition happens even with only two firms.