The Cournot model gave us a way to analyze oligopolistic markets that are somewhere between collusion/monopoly and Bertrand/perfect competition. As in most oligopoly models, equilibrium in the Cournot model came from firms rationally thinking through how other firms in the market are likely to behave in response to their production decisions.

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Importantly, the Cournot model also relies on another assumption whose implications we didn’t think about in much detail, namely, that the firms choose simultaneously. That is, each firm chooses its optimal quantity based on what the firm believes its competitor(s) might do. If it expects its competitor(s) to produce some other quantity, its own optimal action changes—that was the logic of the reaction curve.

If you think about it, though, each company has an incentive to try to choose its output level first and force its competitors to be the one who has to react. The first firm to make its decision could increase its output and say, “Oh well, I have already made more than Cournot says I am supposed to produce. What are you going to do about it?” Because the competitor’s reaction curve slopes downward in this case, the competitor, seeing the high quantity the original firm is producing, would want to reduce its output. Therefore, a first-mover advantage exists in this market.

An oligopoly model in which firms move sequentially—first one, then another, then (if there are more than two firms) another, and so on, is called Stackelberg competition. (Heinrich Freiherr von Stackelberg was an early-twentieth-century German economist who first analyzed this type of oligopoly.) The firm that moves first is sometimes called the Stackelberg leader. To see how sequential competition changes things, let’s revisit our oil producers, Saudi Arabia and Iran.

In that example, the market inverse demand for oil was P = 200 – 3Q, and both countries had a constant marginal cost of $20 per barrel. Each firm produced where marginal revenue equaled marginal cost:

MR_S = 200 – 6q_S – 3q_I = 20

MR_I = 200 – 6q_I – 3q_S = 20

In Cournot competition, we rearranged this equation to solve for each country’s reaction curve:

q_S = 30 – 0.5q_I

q_I = 30 – 0.5q_S

We know that this formula gives the best output a country can choose, taking as given the other country’s output level. Plugging one reaction curve into the other gave us the Nash equilibrium, in which each country produced 20 million bpd at a market price of $80 per barrel.

Now suppose Saudi Arabia is a Stackelberg leader: It chooses its quantity first. What will Saudi Arabia do with this first-mover advantage? (Maybe we think the Saudis are natural first-movers in this market because of their productive capacity. In any case, the results would be the same, albeit with the labels changed, if Iran moved first.)

Iran’s incentives remain unchanged. It still has the same residual demand and reaction curve, and the reaction curve continues to show Iran’s best response to any choice by Saudi Arabia. In Stackelberg competition, however, Iran will know with certainty what Saudi Arabia’s production decision is before it makes its own. Iran reacts optimally to any production choice that Saudi Arabia makes by plugging this value for q_S into its reaction function. Importantly, Saudi Arabia realizes Iran will do this before it makes its first move.

Because Saudi Arabia knows that Iran’s output is going to be a function of whatever Saudi Arabia chooses first, the Saudis want to take that impact into account when they make their initial production decision. In this way, Saudi Arabia can take advantage of being the first-mover. To do so, it plugs Iran’s best response (which it knows from previous experience) into its own demand and marginal revenue curve equations. The fact that the Saudi marginal revenue curve changes means that Saudi Arabia will no longer have the same reaction curve it had in the Cournot model. In that model, Saudi Arabia faced the demand curve

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P = 200 – 3(q_S + q_I)

Now that it is a first-mover in a Stackelberg oligopoly, Saudi Arabia’s demand is

P = 200 – 3q_S – 3q_I = 200 – 3q_S – 3(30 – 0.5q_S) = 200 – 3q_S – 90 + 1.5q_S

Do you see what happened? We substituted Iran’s reaction function (q_I = 30 – 0.5q_S ) directly into the Saudi demand curve. We did this because Saudi Arabia recognizes that, by going first, its output choice affects its demand (and therefore its marginal revenue) both directly and indirectly through its effect on Iran’s production decision. The direct effect is captured by the term – 3q_S in the equation; this effect is the same as in the Cournot model. The indirect effect comes from the impact of Saudi Arabia’s output choice on Iran’s production response. This is embodied in the equation’s second q_S term (1.5q_S ).

We can further simplify this demand curve:

P = 110 – 1.5q_S

We know from Chapter 9 that Saudi Arabia’s marginal revenue curve is then MR_S = 110 – 3q_S. Setting this equal to marginal cost ($20 per barrel) and solving for q_S give Saudi Arabia’s profit-maximizing output in this Stackelberg oliopoly:

MR_S = 110 – 3q_S = 20

3q_S = 90

q_S = 30

As the first-mover, Saudi Arabia finds it optimal to produce 30 million bpd, 10 million more than the Cournot oligopoly output (20 million bpd).

Next, we have to see how Saudi Arabia’s decision affects Iran’s optimal production level. To do that, we plug Saudi Arabia’s output level into Iran’s reaction curve:

q_I = 30 – 0.5q_S = 30 – 0.5(30) = 15

Iran now produces 15 million bpd, rather than 20 as in the Cournot case. By moving first, Saudi Arabia gets the jump on Iran, leaving Iran no choice but to drop its output level from 20 to 15 million bpd.

Therefore, total production is 45 million bpd in the Stackelberg case. This is more than the output produced in the Cournot oligopoly (40 million). And, because production is higher, the market price must be lower under sequential production decisions than under Cournot’s simultaneous-decision framework. Specifically, the price is 200 – 3(30 + 15) = $65 per barrel (instead of the Cournot equilibrium price of $80).

What happens to profit? For Saudi Arabia, profit is 30 × (65 – 20) = $1,350 million/day. This is $150 million more than its $1,200 million/day profit in the (simultaneous-move) Cournot oligopoly. Such an outcome shows us the advantage of being the first-mover. Iran, on the other hand, makes a profit of only 15 × (65 – 20) = $675 million/day, well below its Cournot profit level of $1,200 million/day. In the next chapter on game theory, we discuss the role of first-mover advantage in strategic decision making in more detail. For now, we can already see why firms might want to come into a market early and try to make their production decisions before other firms have a chance.

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Although it’s somewhat abstract and mathematical, the idea of Stackelberg competition in which one firm moves first and obtains an advantage that leads later firms to adjust their strategy and reduce their output is very true to life, as we will see in the next chapter.