Stackelberg Model

Also known as · Stackelberg leadership · sequential quantity competition · sequential pricing

The Stackelberg model is sequential quantity competition. Firm 1 (leader) sets $q_1$ first; firm 2 (follower) observes and responds with its Cournot best-response $q_2(q_1)$ . The leader internalises the follower's reaction by substituting it into its own profit and maximising. For linear demand with constant $MC = c$ :

q_1^* = \frac{A-c}{2}, \quad q_2^* = \frac{A-c}{4}, \quad Q^* = \frac{3(A-c)}{4}.

The leader produces more and earns more than in Cournot; the follower produces less and earns less. First-mover advantage.

type: reaction-functions
br1: 4,-0.5
br2: 4,-0.5
points: Stackelberg|The leader moves first and picks its best point on the follower's BR: q₁ = (A − c)/2.|4,2

When to use

Use Stackelberg whenever firms move sequentially in quantities — capacity-commitment games, industries with a dominant incumbent and a follower, sequential entry deterrence. The mechanical recipe: solve the follower's problem (the Cournot Best Response Function), substitute into the leader's profit, take the leader's FOC, then back out the follower's quantity. The commitment is the whole advantage — it only works because the leader moves first and cannot be undone.

Stackelberg Model

When to use

Appears in