Stackelberg Model

The Stackelberg model is a sequential-move duopoly framework in which one firm (the leader) commits to an output quantity before its rival (the follower) chooses its own quantity in response. It was developed by German economist Heinrich von Stackelberg in his 1934 work Marktform und Gleichgewicht (Market Structure and Equilibrium).

The model differs from the simultaneous-move Cournot model by introducing a first-mover advantage. The leader, knowing the follower will optimize against whatever quantity it chooses, incorporates the follower's reaction function into its own profit-maximization problem. Solving by backward induction:

• The follower observes the leader's output q₁ and picks q₂ to maximize its profit, yielding a reaction function q₂(q₁).
• The leader anticipates this and chooses q₁ to maximize profit given q₂(q₁).

In the standard linear-demand, constant-marginal-cost case, the leader produces more than it would under Cournot competition, the follower produces less, total industry output is higher, and the market price is lower than the Cournot outcome but higher than perfect competition. The leader earns higher profits than the follower — the first-mover advantage — provided its commitment is credible and observable.

For political-economy and IR researchers, the Stackelberg logic extends well beyond firms. It is widely used to model:

• Trade policy: a large economy setting tariffs before smaller trading partners respond.
• Monetary and fiscal interaction: a central bank moving before fiscal authorities, or vice versa.
• Security and arms competition: a dominant power setting force levels that rivals then react to.
• Climate negotiations: early commitments by major emitters shaping followers' pledges.

Key assumptions limit the model's realism: the leader's commitment must be observable and irreversible, information about the follower's costs and demand must be reliable, and there must be a clear sequence of moves. When commitments can be revised, the equilibrium can unravel toward the Cournot outcome. Extensions include Stackelberg price competition, multi-follower games, and Stackelberg equilibria in general game-theoretic settings.