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# Bertrand Competition

## Game Description

In each round, each firm in a group simultaneously announces a price for a homogenous good (course notes for a difficult course). All demand goes to the firm announcing the lowest price, subject to optional capacity constraints. At the end of each round, the lowest price and market profits are revealed.

### Learning Objective 1: The Bertrand Paradox

A market for a homogenous good without capacity constraints leads to vigorous price competition and marginal-cost pricing in equilibrium.

### Learning Objective 2: Maintaining Collusion

Communication and indefinite repetition facilitate collusion.

### Learning Objective 3: Meet the Lowest Price Policies

Firms committing to selling at the lowest advertised price may lead to collusive outcomes.

## Brief Instructions

Market demand is Q(P)=3600-200P, and costs are MC=\$2, meaning Q=3200 maximizes surplus. The monopolist would choose {P=\$10;Q=1600} as inverse demand is P(Q)=18-Q/200.

Announcing the monopolist's price focuses students on the game's strategic implications. With students not primed for collusion, almost all duopolies will converge to prices near marginal cost in a few rounds. Convergence will be even stronger in larger groups.

## Key Treatment Variations

1. #### Capacity Constrants

Reducing the returns to vigorous price competition, capacity constraints are an important reason why price competition does not lead to marginal-cost pricing in many markets.

Checking the Capacity Constraint option sets market capacity equal to 2400 units, equally divided between each firm in a group. Halfway between the monopoly and perfect competition quantities, it results in an equilibrium price of \$6.

2. #### Collusion Maintenance

To facilitate collusion, set Group Size equal to 2, enable Chat and have indefinite repetition (e.g., set Minimum Rounds to 2 and Ending Probability to 50%). Make sure students know they can chat but do not know the number of rounds. To make collusion difficult, increase group size, disable chat and announce the number of rounds.

3. #### Price Matching

Students are often surprised to learn that firms agreeing to meet the lowest advertised price in a market may have anti-competitive effects.

When you check Allow Price Matching, in each round each firm not only chooses its price, but also chooses whether it agrees to meet the lowest price chosen by its competitors. Competitors agreeing to price match now instantaneously best respond a firm’s price cuts, thus reducing the payoff from such cuts.

## Results

The results will help you highlight the pull of marginal-cost pricing in Bertrand markets

The first set of graphs (Figure 1) show the by round evolution of prices across all groups. In each graph, a box-and-whiskers plot is displayed for each round. (The boxes span the 25th and 75th quartiles, with a line indicating the median. The whiskers extend to the the extreme values.) Market Prices Across Rounds include only those prices resulting in sales, whereas Prices Announced Across Rounds includes all announced prices (whether or not any were sold at that price).

The next set of results (Figure 2) allow you to focus on particular groups. The Group Summary Table displays, for each group, average and final-round surpluses. Marginal cost pricing results in 100% efficiency (i.e., total surplus maximized), and thus a quickly converging group registers average efficiency (across all rounds) closer to 100%.

To dig more deeply into the prices announced by a particular group, click the radio button next to the Group Number in the table. The resulting graph will indicate the choice of each student in each round.

Note that you can select which elements to include in the graph by clicking the checkboxes next to the label in the legend.