Stackelberg Model
What is Stackelberg Model?
The Stackelberg model is an oligopoly model where a leader firm sets output first and a follower firm then chooses its output in response.
Unlike Cournot's simultaneous choices, the Stackelberg leader moves first and, anticipating the follower's reaction, produces more than in Cournot to grab market share, earning higher profit. The follower produces less. Solved by backward induction, it gives the leader a first-mover advantage in quantity competition and produces a total output above the Cournot level (closer to competitive output).
Stackelberg Model: a worked example
Two firms face market demand P = 130 - Q, each with constant marginal cost of $10. The follower's profit is (130 - qL - qF - 10)qF, which gives the reaction function qF = 60 - qL/2. Substituting that into the leader's residual demand, the leader maximizes (60 - qL/2)qL, which yields qL = 60. The follower then produces 60 - 30 = 30. Total output is 90, price is $40, and the margin is $30. The leader earns $30 x 60 = $1,800; the follower earns $30 x 30 = $900. Under Cournot each firm would make 40 units and earn $1,600, so moving first is worth $200 to the leader.
The mistake students make with stackelberg model
A common error is thinking the leader wins by staying flexible and reacting once it sees the follower's output. The advantage runs the other way: the leader gains only because its quantity is an irreversible commitment the follower must take as given. Let the leader quietly revise afterward and the game collapses back to Cournot. The second slip is assuming the industry does better overall; in the example, combined profit falls from $3,200 under Cournot to $2,700, because the leader's expansion drags the price down.
Stackelberg Model questions
What is the difference between stackelberg and cournot competition?
Stackelberg and Cournot differ only in timing. Cournot firms choose output simultaneously, so neither can commit first; the Stackelberg leader chooses and the follower observes before responding. That one change raises the leader's output and profit, cuts the follower's, and lifts total industry output, so the market price ends up below the Cournot level and closer to the competitive one.
How do you solve a stackelberg model?
Solving a Stackelberg model takes two rounds of backward induction. First derive the follower's reaction function by maximizing its profit with the leader's quantity treated as a fixed number. Then substitute that reaction function into the leader's residual demand and maximize the leader's profit over its own output. Plug the leader's answer back into the reaction function for the follower's quantity, then add both to find market price.
Is the stackelberg leader always better off?
The Stackelberg leader is always at least as well off as under Cournot in the standard quantity-setting model, since it can simply choose the Cournot quantity and do no worse. That guarantee rests on two assumptions: the follower genuinely observes the leader's choice, and the leader cannot revise it later. Remove either one and the first-mover advantage disappears.
Formula / Example
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