Stackelberg Competition

Game Theory · Axiom Academy

LESSON Stackelberg Competition In Stackelberg competition, the game unfolds sequentially. Firm 1 (the leader) commits to producing quantity q₁. Firm 2 (the follower) observes q₁ and then chooses its best response q₂. This timing creates a strategic advantage: the leader can anticipate how the follower will react and incorporate this knowledge into its decision. We solve by backward induction. First, find the follower's optimal response for any given q₁. The follower maximizes its profit, taking q₁ as given. With inverse demand P = a - Q (where Q = q₁ + q₂) and marginal cost c, the follower's profit is: The follower's best response function shows how q₂ depends on q₁: The leader anticipates the follower's best response and incorporates it into its own profit maximization. Substituting the follower's response function into the leader's profit: The leader chooses q₁ to maximize this profit, knowing that the follower will respond optimally. Solving the leader's first-order condition and then substituting back into the follower's best response gives the Stackelberg equilibrium quantities: Notice that the leader produces more than the follower. This is the first-mover advantage in action. 5. First-Mover Advantage vs. Cournot Compare to Cournot equilibrium (simultaneous moves) where both firms produce (a-c)/3:

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