5.6 Oligopoly

[5.2 Using Game Theory] [5.3 Classic Game Models]

[5.5 Sequential Games] [5.7 Network Effects]

An
oligopoly is a market with only a few sellers. Airlines, soft drinks,
supermarket chains and car manufacturing are all examples of oligopoly. Firms
in these markets are neither monopolists nor are there so many that competition
is perfect or close to it.

Thus far
in this segment, we have considered games that present oligopolistic
competition in relatively simple terms. Rival firms could choose between
colluding or competing or between advertising and not advertising. In reality,
competition in an oligopoly is more complex. This is because firms can choose
from a wide range of prices and production decisions.

Game
theory is equipped to handle these more complex situations. This topic will
introduce you to two game-theoretic models that capture the interaction between
firms in an oligopoly.

To
understand the behaviour of a firm in an oligopoly, consider a duopoly market
for flowers with two sellers, Bill and Ben. Suppose they are initially
producing 40 flowerpots each, so that the market price is $40 per pot. Bill is
considering producing more.

However,
this will be profitable only if price does not fall by too much. This depends
on how Ben might react to Bill’s increased production. Bill conjectures that
there are two ways Ben may react:

·
*Reducing price to maintain quantity
sold.* Ben might be
concerned about the reduction in his sales quantity as a result of Bill’s
increased production. In order to maintain his existing volume, Ben could
reduce his price.

·
*Reducing production to maintain
market price.*
Alternatively, Ben might be worried about the potential drop in the market
price of flowers when Bill increases his output. He realises that, if he cuts
back production, he can maintain the existing price in the market.

It is
possible that Ben’s reactions might be more complicated. Economists, however,
have found that focusing on reactions that maintain price or quantity
simplifies the analysis of oligopoly. In effect, they define two distinct
theories of competition — Cournot quantity
competition and Bertrand price competition. We will examine each in turn. As we
will see, because Bill anticipates price matching by Ben under Cournot competition but not Bertrand competition, the
former results in higher equilibrium prices than the latter.

Suppose
that Bill believes that Ben will always maintain his current level of output.
That is, he believes that Ben will let the price of flowers fall rather than
reduce his output.

This
belief is the basis of Cournot quantity competition.
This competition is named after Augustin Cournot who, in 1838, was the first person to attempt to
model oligopolistic competition. It is called
quantity competition because each firm believes that its rivals will always act
to maintain their current quantity.

The
following table highlights the decision facing Bill. If Ben is producing 20 pots
of flowers, then Bill knows that demand for his flowers is simply the market
demand less a quantity of 20 pots. This is because for every level of
production he chooses, Ben will adjust his price so that the difference between
market demand at that price and Bill’s production is exactly 20 pots. The
individual demand schedule for Bill’s flowers is simply the market schedule
less 20 pots.

**Table
1: Bill’s profit maximisation decision when Ben produces 20 litres.**

Ben’s quantity (pots) |
Bills’s quantity (pots) |
Market quantity (pots) |
Price ($) |
Bill’s total revenue (and total profit) ($) |

20 |
0 |
20 |
100 |
0 |

20 |
10 |
30 |
90 |
900 |

20 |
20 |
40 |
80 |
1600 |

20 |
30 |
50 |
70 |
2100 |

20 |
40 |
60 |
60 |
2400 |

20 |
50 |
70 |
50 |
2500 |

20 |
60 |
80 |
40 |
2400 |

20 |
70 |
90 |
30 |
2100 |

20 |
80 |
100 |
20 |
1600 |

20 |
90 |
110 |
10 |
900 |

20 |
100 |
120 |
0 |
0 |

To
maximise profits, Bill will follow the same rule we discussed in Segment 4.3
for a monopolist — he will choose a quantity that equates his marginal revenue
and marginal cost. As Bill’s marginal cost is zero in this example, he will maximise
profits by maximising total revenue. From the above table, if Ben is producing
20 pots, Bill will produce 50 pots to maximise his profit.

What if
Bill believes that Ben will produce 60 flowerpots? This is shown in the
following table.

**Table
2: Bill’s profit maximisation decision when Ben produces 60 litres.**

Ben’s quantity (pots) |
Bill’s quantity (pots) |
Market quantity (pots) |
Price ($) |
Bill’s total revenue (and total profit) ($) |

60 |
0 |
60 |
60 |
0 |

60 |
10 |
70 |
50 |
500 |

60 |
20 |
80 |
40 |
800 |

60 |
30 |
90 |
30 |
900 |

60 |
40 |
100 |
20 |
800 |

60 |
50 |
110 |
10 |
500 |

60 |
60 |
120 |
0 |
0 |

Because
Ben is producing more, Bill has to produce less to maintain a given market
price. The individual demand schedule facing Bill is lower and Bill’s profit
maximising output level is now only 30 pots of flowers.

Notice
that when Bill believes that Ben is going to produce more, he will react by
producing less. The more Ben is going to produce, the smaller the share of the
market available to Bill. So Bill reacts by limiting his own output to maintain
the market price and maximise his own profits.

Table 1
(above) shows how Bill’s output choice will alter with Ben’s production
decision. The upper part shows how Bill’s individual demand curve depends on
Ben’s output choice. If Ben produces 20 pots, then Bill’s individual demand
curve is given by *D*_{1} — the market demand shifted left by 20 pots.
Bill will maximise profits by producing 50 pots of flowers. This is where the
relevant marginal revenue curve *MR*_{1} intersects with marginal cost. Remember that
marginal cost is zero in this example. The lower part then plots this decision.
Bill produces 50 pots when Ben produces 20 pots.

If Ben
increases production to 60 pots, then this reduces Bill’s individual demand
curve. This is shown by curve *D*_{2}.
Again Bill maximises profits by producing where marginal revenue equals
marginal cost. But because Ben is producing more, Bill’s marginal revenue at
each level of output is less. This is shown by the curve *MR*_{2}.
Bill’s profit-maximising response to Ben’s production is then shown in the
lower part. When Ben produces 60 pots of flowers, Bill wants to produce only 30
pots.

Bill’s *reaction curve*, shown in the lower part
of Figure 1 (below), shows Bill’s profit-maximising level of output for every
output level chosen by Ben. If Ben produces nothing, then Bill is a monopolist
and will produce the monopoly output, 60 pots. If Bill expects Ben to flood the
market and sell 120 pots, then it is not worthwhile for Bill to produce
anything. In between, if Ben produces 20 pots, Bill will produce 50, and if Ben
produces 60 pots, Bill will produce 30.

**Figure 1**

If Ben
holds similar beliefs to Bill — that is, that Bill will always act to maintain
his existing output level — then he will have a reaction curve with a similar
property to Bill’s. That is, Ben will always want to decrease (increase) his
output as Bill increases (decreases) his.

We can
place Bill’s and Ben’s reaction curves on the same diagram. This is done in
Figure 2. This allows us to determine the Nash equilibrium in Cournot quantity competition. Recall that the choice of
strategies for two players is a Nash equilibrium if neither player can gain by
changing to another strategy. In this case, in the choice of quantities, a Nash
equilibrium occurs if neither Bill nor Ben wishes to change their output,
assuming that the other acts to keep his or her output the same.

In Figure 2, the only Nash equilibrium is where Bill and Ben both choose
40 pots of flowers each.
If Bill were to choose
20 pots, Ben will want to choose
50 pots — the corresponding point on his reaction curve.
However, these choices of output are not a Nash equilibrium because, while
Ben is happy with his choice, Bill can improve
his profits by choosing an output of 35 pots.
This corresponds to a point
on his reaction curve. Unless
both Bill and Ben are choosing outputs
on their reaction
curves, each is not maximising profits given the choice of the other.
Hence, only points
where reaction curves
coincide represent a Nash equilibrium.

Figure 2

Note that
the Cournot equilibrium involves total production of
80 pots, more than the monopoly output of 60 pots. It also involves less
production than under perfect competition. In this example, the perfectly
competitive output would be 120 pots with a price equal to the marginal cost of
zero.

What if
Bill believes that Ben will always act to maintain his price rather than his
quantity of sales? This situation is illustrated by Bertrand price competition.
Joseph Bertrand, when reviewing Cournot’s work in
1883, noticed that a different conclusion could arise when firms believe that
rivals will act to maintain price rather than output. It is called price
competition for this reason. Indeed, it is easier to analyse Bertrand price
competition by examining firms’ pricing choices rather than their output
choices.

To see what
happens in price competition, imagine that Ben currently sells flowers at $50
per pot. He will sell as much or as little as he needs to maintain this price.
Now if Bill sets his price at, say, $60, he will find himself unable to sell
any flowers. This is because flowers, from the point of view of consumers, are
a homogenous product. Hence, consumers will purchase from the firm that sells
at the lowest price. With Bill setting his price at $60, Ben is able to capture
the entire market (a quantity of 70 pots). Bill earns no profits.

Can Bill
do better than this by changing his price, given that he believes that Ben will
maintain his price at $50? Suppose that Bill lowers his price and undercuts
Ben. For example, Bill could lower his price to $40. As Bill is selling flowers
more cheaply than Ben, he will capture the entire market. Bill will sell 800
pots and make $3200 in profit. Ben, in contrast, will make no sales and earn no
profit. Bill is better off undercutting Ben than by pricing above him.

What is true
for Bill is true for Ben. If he prices below Bill, he earns more than if he
prices above him. What this means is that both Bill and Ben will find it
advantageous to react to the other’s price by lowering their own price.

When Bill
and Ben have reactions that involve undercutting each other’s price, what will
be the Nash equilibrium prices? It turns out that, in this situation, there is
one Nash equilibrium price — a price equal to marginal cost which is zero. To
see why this is the case, we need to reason in steps. Consider the following:

1.
It cannot be a Nash equilibrium for Bill to charge a
different price than Ben. If this were to occur, the person with the higher
price could always earn more profits by lowering price and undercutting rivals.

2.
It cannot be a Nash equilibrium for Bill and Ben to
charge the same price at some level above marginal cost. If this were to
happen, then either Bill or Ben could gain the entire market by charging a
slightly lower price. By making a small price cut, either Bill or Ben can steal
all the other flowers seller’s customers and increase his or her own profit.

3.
It cannot be a Nash equilibrium for Bill or Ben to
charge a price lower than marginal cost (in this case, zero). They would make a
loss by selling at such a price and would prefer not to produce at all.

Given
these three steps, we must conclude that the only Nash equilibrium is where
Bill and Ben charge the same price for flowers equal to marginal cost — in this
case, zero.

In our
example, Bertrand competition leads to a startling conclusion. Even with only
two firms, each firm in equilibrium will set a price equal to marginal cost —
the same as under perfect competition. This result holds whenever production
involves constant marginal costs. Bertrand price competition will always lead
to the same outcome as perfect competition in this case.

Cournot
and Bertrand competition yield markedly different outcomes. Bertrand price
competition leads to outcomes close to those of perfect competition. In
contrast, Cournot pricing outcomes are in between
perfect competition and monopoly pricing.

Both
types of competition are theoretical possibilities. Which one is more
applicable depends on the situation. Remember that each involves firms having a
different type of belief about their competitors. In Cournot,
firms believe rivals will act to maintain output, whereas in Bertrand, they
believe that their rivals’ price will remain fixed.

Cournot
beliefs will be more appropriate in industries where it is difficult for firms
to actually change their output levels. This could occur when firms have
limited production capacities, face rigid production technologies or
manufacture to maintain an inventory stock rather than to supply customers’ orders.

Bertrand
competition is more likely when firms compete directly over price before
setting output. For example, when tendering for a one-off project, like
building a major highway in a large city, competitors face a situation like
Bertrand price competition. The firm with the lowest bid wins the tender and
gets to build the project and the losers get nothing.

Click on
the link here to examine quantity competition in the world memory chip market.

**Topic Summary **

In this
topic you have learnt how to

·
represent
competition between oligopolists as games

·
consider
the difference in outcomes when firms choose quantities rather than prices as a
strategic variable

·
evaluate
when firms can make quantity commitments

Now go on to topic 5.7, “Network Effects”.