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.

Anticipating your competitor’s response

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.

Cournot Quantity Competition

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 D₁ — 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 MR₁ 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 D₂. 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 MR₂. 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.

Bertrand Price Competition

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.

Comparing Cournot and Bertrand Competition

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.