Bertrand Competition

(The contents of this page are provided by the Finance and Economics Experimental Laboratory at the University of Exeter.)

Stand-alone demonstration - Try out this multi-player experiment by making decisions against pre-existing results from a real session. 

Example subject instructions - View subject instructions.

• Level: Year ?1 undergraduate
• Pre-requisite knowledge: ?
• Suitable modules: ?

Abstract

In the standard Bertrand competition game, students play together in small groups as sellers who compete to supply a single buyer (the computer) who always purchases from the seller demanding the lowest price. Sellers choose their prices simultaneously without knowing the prices chosen by others. The goods are perfect substitutes. The demand function is linear, inversely related to price and known to all sellers. The cost of production is the same for all sellers. Students play multiple rounds and there are options for fixed or random pairings.

There is also a setting where the goods are perfect complements. Here, the demand function is once again linear but this time inversely related to the sum of the prices charged by all sellers and the buyer is obliged to purchase an equal quantity from each seller. There is also a monopoly option where each student plays alone against the computer.

Intended Learning Outcomes

1. Bertrand competition drives prices down to marginal cost in a market with many sellers.

2. If there are fewer sellers and opportunities for collusion, higher prices may be achievable.

3. Splitting a monopoly in two can actually be worse for the consumer.

Discussion of Likely Results

In the default setup, sellers have a production cost of £3.00 for each unit sold and may set prices in the range £3.00 to £15.00. The buyer purchases a quantity of 15-P units, where P is the price.

In standard Bertrand competition, P is the lowest price charged. With a small group size (2 or 3 students only) and fixed pairings, there is an opportunity for collusion to develop and P may stay significantly above £3. If this is followed by a second treatment with a larger group size (4 or more students) and random pairings, P quickly drops very close to £3 although the average price may be higher due to failed attempts at collusion.

In the monopoly situation, P is the price set by the monopolist, who makes a profit of (15-P)(P-3), which is maximised by charging a price of £9. Let the monopoly be split in two, where the two duopolists sell perfect complements, each have a production cost of £1.50 and the demand function is 15-(P1+P2), where P1 and P2 are the two prices charged. Now each duopolist i has profit (15-(Pi+Pj))(Pi-1.5) This is maximised at Pi=(16.5-Pj)/2. Thus, we find P1=(16.5-P2)/2 and P2=(16.5-P1)/2. The equilibrium has P1=P2=5.5 so the consumer pays £11 instead of £9. This is suggesting that consumers might not necessarily benefit from anti-trust measures, e.g. breaking up Microsoft into two mini-Bills.