Cournot Competition Guide

May 2024 · 5 minute read
Cournot Competition Guide

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In each round, each firm in a group simultaneously chooses its production for a homogenous good (barrels of oil). Market price is determined by a linear demand curve (with slope equal to -1). At the end of each round, a firm learns market production and price (and thus its profits).

Learning Objective 1: Payoff Interdependence in Oligopolies

In a market with relatively few sellers, a firm’s payoff from an action depends on the actions taken by its rivals.

Learning Objective 2: Cournot Nash Equilibrium

When a limited number of firms choose quantities of a homogenous good with price adjusting to sell all units, Nash equilibrium market quantity falls between the monopoly and perfect competition quantities.

Learning Objective 3: Maintaining Collusion

Students experience the tension between maximizing their own profit and cooperating with others to improve profits (i.e., collusion). Communication and indefinite repetition facilitate collusion.

With repetition in a group not primed to collude, group production will normally fall between the monopoly and perfect competition quantities. To make the strategic interaction more salient, we recommend keeping Group Size relatively small (e.g., 5 or fewer).

In a multi-round game (Minimum Rounds > 1 and/or Ending Probability < 100%) the composition of each group remains fixed. To mitigate repeated-game effects, set Number of Rounds to 1. When all groups are done, click Finish, then Replay. Choosing Random randomly assigns groups.

We use a linear demand curve with slope equal to -1, which means that Market Capacity is the intercept of both the horizontal and vertical axes. Therefore, in the Nash equilibrium of the one-round game, each firm produces

$${\small q^{\text{Nash}}=\frac{\text{Market Capacity }-\text{ Marginal Cost}}{\text{Group Size }+ 1}.}$$

As students are restricted to integer choices, integer Nash quantities are desirable. Also, when considering collusion, it is desirable that an even split of the monopolist’s choice is an integer. The default game (Market Capacity=30; Marginal Cost=6) works very well for group sizes of 1, 2 or 3 (Nash quantities are 12, 8 and 6, respectively.) For Group Size=4, consider parameters so that Market Capacity - Marginal Cost=40.

Finally, if you change default parameters, keep in mind the implication for Maximum Production, the maximum quantity a firm can produce in a round. We recommend setting it equal to Market Capacity/Group Size (rounding down if not an integer) so that firms can exceed equilibrium production but not exceed maximal market demand (although if group production does exceed market capacity, then market price will be 0.)

  • Collusion Maintenance

    This game allows your students to experience the tensions involved in maintaining collusion. Smaller Group Size, enabling Chat and indefinite repetition (i.e., Ending Probability < 100%) all facilitate collusion (make sure students know they can chat and know that they do not know the number of rounds). You might also point out a collusive outcome (e.g., the even split of the monopolist’s quantity). To make collusion difficult, increase group size, disable chat and set a finite number of rounds.

  • Monopoly

    To implement a monopoly, change Group Size to 1. Setting the firm's Maximum Production equal to Market Capacity ensures that the student can investigate quantities above and below the profit maximizing quantity (equal to (Market Capacity - Marginal Cost)/2).

  • For the primary teaching goals, you will want to show convergence towards the Nash Equilibrium quantity over multiple rounds. This convergence can be studied at the individual level through our Production graph (Figure 2) or at the group level through our Group Quantity graph (Figure 3).

    If you have played multiple games, you can use the View menu (Figure 1) to select which game you want to study in the playlist. To choose whether you want to study it at the aggregate or round-level, you can use the View button. The Results available for each view are divided into three tabs: the Graphs, Tables, and Raw Data. The detailed displays of each tab, we will provide below. Lastly, if you used one of the Replay options, you can use the Comparison button to compare these linked games side-by-side.

    Assuming you have selected the Aggregate view, the Graphs tab will display the Production graph (Figure 2), summarizing all production choices across the groups and rounds for this game, and the Group Quantity graph (Figure 3), summarizing the same but at the group level. These two graphs provide you with the main teaching points of showing how the production decisions fall in between the Monopoly Quantity and Competitive Quantity and tend towards the Nash Equilibrium Quantity.

    Assuming you have selected the view of a particular round, the results will display the Production graph (Figure 4), summarizing all production choices across the groups within the round, and the Group Quantity graph (Figure 5), showing the distribution of the group choices within the round. Additionally, we provide you with the Individual Quantity graph (Figure 6), showing the distribution of the individual choices within the round. These three graphs provide you with a greater level of detail to showcase the data at the individual round level.

    The Tables tab will display the Game Configuration and Action tables (Figure 7) and Welfare tables (Figure 8). These tables show you the key statistics for interpreting the data at the group and individual level such as the mean, the median production quantitites, and the percentage of groups and players producing the Monopoly or Nash Equilibrium Quantity. The Welfare table gives some additional insight into the effects on surplus.

    The Raw Data tab will display the Raw Data table (Figure 9) which simply displays the quantity production decisions at the chosen level.

    For the explanation of our Tables and Raw Data tab, we take the examples from the Aggregate view but the Round view is analogous.

    In the first round, robots choose the symmetric Nash Equilibrium quantity with some random variation. In each subsequent round, the robot best responds to the sum of other player's quantity choices from the previous round.

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