Stackelberg Competition

A sequential duopoly in which a leader commits to an output and the follower best-responds.

Ask the Game theory assistant1 min read · Updated September 9, 2026

Definition

Leader chooses $q_1$ to maximize $\pi_1(q_1,q_2^*(q_1))$ where $q_2^*(q_1)\in\arg\max_{q_2}\pi_2(q_1,q_2)$ is the follower's best response.

The solution concept is subgame perfect equilibrium, obtained by backward induction.

Intuition

Committing first can be valuable — the leader exploits the follower's rational response.

First-mover advantage arises when best responses slope downward.

Worked example

With linear demand $P=a-Q$ and zero cost, Stackelberg yields $q_1=a/2$ , $q_2=a/4$ , giving profits $a^2/8$ and $a^2/16$ — the leader earns more than Cournot's $a^2/9$ .

Security games deploy randomized commitments against best-responding attackers (Stackelberg security).

The math

Leader's program is a bilevel optimization $\max_{q_1}\pi_1(q_1, q_2^*(q_1))$ — generally nonconvex but tractable in standard demand systems.

Without commitment power, the game collapses to simultaneous Cournot.

Where it is used

Industrial organization, pricing, and entry deterrence.

Stackelberg security games deploy patrol schedules at airports (ARMOR, IRIS).

More in Game theory

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