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# Cournot Competition

## Game Description

In each round, each firm in a group simultaneously chooses its production for a homogenous good (scooters). 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.

## Brief Instructions

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-period 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.)

## Key Treatment Variations

1. #### Collusion Maintenance

This game allows your students 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.

2. #### 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).

## Results

Results are presented per round. To switch between rounds, use the Go To: drop-down menu (Figure 1).

For each round, the top Group Profit panel, which is closed by default, displays a table (Figure 2) allowing you to compare each group's outcome to three benchmarks: the profit-maximizing monopolist, perfect competition, and the Nash equilibrium. In addition to market and average quantities and resulting market price, the table also presents producer, consumer and total surpluses.

The Production Graph (Figure 3) plots each group’s total production along the market demand curve. By also showing the monopolist's quantity (i.e., perfect collusion) and the Nash equilibrium total quantity, this graph summarizes market outcomes relative to these benchmarks. With repetition, you should see groups move towards the Nash prediction.

By clicking on the boxes next to the legend items, you can dynamically choose which items to include in the graph.

## Robot Play

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.