6.2 Stackelberg Leadership Model

The Stackelberg Leadership Model explores how firms gain an edge by moving first in a market. It shows how a leader firm can maximize profits by anticipating and influencing a follower's decisions, like Coca-Cola entering a new market before Pepsi.

This model reveals key differences from the Cournot model, where firms move simultaneously. In Stackelberg, the leader produces more, the follower less, and total output is higher. This dynamic shapes strategies for both leaders and followers in real-world markets.

Stackelberg Leadership Model

Concept of first-mover advantage

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• First-mover advantage occurs when one firm (leader) makes its output decision before the other firm (follower)
  • Leader firm anticipates the follower's reaction and incorporates this information into its own output decision, allowing the leader to choose a point on the follower's reaction curve that maximizes the leader's profits (Coca-Cola entering a new market before Pepsi)
• Sequence of moves in the Stackelberg model involves the leader firm choosing its output level first, followed by the follower firm observing the leader's output and then choosing its own output level (Apple releasing a new iPhone model, then Samsung deciding on its Galaxy production)
• Leader's first-mover advantage is only effective if its output choice is irreversible, serving as a credible commitment
  • If the leader can change its output after observing the follower's choice, the game collapses into a simultaneous-move Cournot model (OPEC announcing oil production cuts, then increasing production after observing non-OPEC countries' output)

Calculation of Stackelberg equilibrium

• Assumptions include two firms producing a homogeneous product, a linear demand curve $P = a - b(q_1 + q_2)$, and constant marginal costs $MC_1$ and $MC_2$ for the leader and follower, respectively
• Follower's reaction function is derived by maximizing profits given the leader's output $\max_{q_2} \pi_2 = (P - MC_2)q_2$, resulting in the follower's best response $q_2 = \frac{a - MC_2}{2b} - \frac{q_1}{2}$
• Leader's output decision maximizes profits by incorporating the follower's reaction function $\max_{q_1} \pi_1 = (P - MC_1)q_1$, yielding the leader's optimal output $q_1^* = \frac{a - 2MC_1 + MC_2}{2b}$
• Stackelberg equilibrium quantities are:
  1. Leader's quantity: $q_1^* = \frac{a - 2MC_1 + MC_2}{2b}$
  2. Follower's quantity: $q_2^* = \frac{a - 3MC_2 + 2MC_1}{4b}$

Stackelberg vs Cournot outcomes

• Cournot model outcomes with simultaneous moves:
  • Cournot equilibrium quantities: $q_1^C = q_2^C = \frac{a - 2MC_i + MC_j}{3b}$, where $i,j \in {1,2}$ and $i \neq j$
  • Total industry output: $Q^C = \frac{2a - MC_1 - MC_2}{3b}$
• Stackelberg model outcomes with sequential moves:
  • Leader's quantity: $q_1^* = \frac{a - 2MC_1 + MC_2}{2b}$
  • Follower's quantity: $q_2^* = \frac{a - 3MC_2 + 2MC_1}{4b}$
  • Total industry output: $Q^S = \frac{3a - 2MC_1 - MC_2}{4b}$
• Comparison of outcomes reveals that the leader's output in Stackelberg is higher than its Cournot output $q_1^* > q_1^C$, while the follower's output in Stackelberg is lower than its Cournot output $q_2^* < q_2^C$
  • Total industry output is higher in Stackelberg than in Cournot $Q^S > Q^C$, and the leader's profits are higher in Stackelberg, while the follower's profits are lower compared to Cournot (Walmart as a leader and smaller retailers as followers in the retail industry)

Strategic implications for leaders and followers

• Advantages of being the leader include higher profits compared to the Cournot model, ability to influence the follower's output decision, and market share advantage (Amazon's early dominance in e-commerce)
• Disadvantages of being the leader involve the requirement of a credible commitment to the announced output level and the potential for the follower to develop strategies to become the leader through capacity investments or product differentiation (Netflix's original content production to challenge traditional media leaders)
• Advantages of being the follower include flexibility to adjust output based on the leader's decision and the possibility to benefit from the leader's market development efforts in advertising or R&D (Generic drug manufacturers entering the market after patent expiration)
• Disadvantages of being the follower are lower profits compared to the leader and the Cournot model and a reactive rather than proactive market position (Small smartphone manufacturers following Apple and Samsung's lead)
• Strategic considerations:
  1. Firms may engage in various strategies to secure the leader position, such as capacity investments, product differentiation, or strategic partnerships (Toyota's investments in hybrid technology to lead the automotive industry)
  2. In some cases, firms may prefer to be the follower when market development costs are high or when there is uncertainty about demand (Local restaurants following the menu trends set by national chains)
  3. The timing of moves and the credibility of commitments are crucial factors in determining the outcomes of the Stackelberg model (Boeing and Airbus' long-term production commitments for new aircraft models)