Stackelberg Competition: The Advantage of Moving First

In chess, moving first is a small advantage. In business, moving first can be worth billions.

• Amazon dominated e-commerce by moving first
• Google captured search by moving first
• Facebook dominated social networking by moving first

But moving first isn’t always good:

• Microsoft’s Zune failed against the iPod
• Google+ failed against Facebook
• Many “first-mover” startups fail while fast followers succeed

When does moving first help? When does it hurt?

Stackelberg competition provides the game-theoretic framework to answer these questions.

Sequential vs Simultaneous Competition

Simultaneous competition (Cournot/Bertrand):

• Firms choose strategies at the same time
• Neither observes the other’s choice before deciding
• Nash Equilibrium outcome

Sequential competition (Stackelberg):

• One firm (the leader) moves first
• The other firm (the follower) observes the leader’s choice, then responds
• Subgame perfect equilibrium outcome

The key difference: In Stackelberg competition, the leader can commit to a strategy, and the follower must respond optimally.

The Stackelberg Duopoly Model

Setup:

Two firms produce identical products.

Market demand: $P(Q) = a - b \cdot Q$ where $Q = q_1 + q_2$

Costs: Constant marginal cost $c$ for both firms

Sequence:

1. Leader (Firm 1) chooses quantity $q_1$
2. Follower (Firm 2) observes $q_1$, then chooses $q_2$
3. Market clears at price $P(q_1 + q_2)$
4. Profits realized

Solving by Backward Induction

Step 1: Follower’s optimization

Given leader’s quantity $q_1$, follower maximizes profit:

$$\pi_2(q_2 | q_1) = [P(q_1 + q_2) - c] \cdot q_2$$ $$= [a - b(q_1 + q_2) - c] \cdot q_2$$

First-order condition:

$$\frac{\partial \pi_2}{\partial q_2} = a - b \cdot q_1 - 2b \cdot q_2 - c = 0$$

Follower’s best response function:

$$q_2^*(q_1) = \frac{a - c - b \cdot q_1}{2b}$$

Interpretation: The more the leader produces, the less the follower produces (quantities are strategic substitutes).

Step 2: Leader’s optimization

Leader knows follower will respond with $q_2^*(q_1)$, so leader maximizes:

$$\pi_1(q_1) = [P(q_1 + q_2^*(q_1)) - c] \cdot q_1$$

Substituting $q_2^*(q_1)$:

$$\pi_1(q_1) = \left[a - b \left(q_1 + \frac{a - c - b \cdot q_1}{2b}\right) - c\right] \cdot q_1$$

Simplifying:

$$\pi_1(q_1) = \left[\frac{a - c}{2} - \frac{b \cdot q_1}{2}\right] \cdot q_1$$

First-order condition:

$$\frac{\partial \pi_1}{\partial q_1} = \frac{a - c}{2} - b \cdot q_1 = 0$$

Stackelberg equilibrium quantities:

$$q_1^* = \frac{a - c}{2b}$$

$$q_2^* = \frac{a - c - b \cdot q_1^*}{2b} = \frac{a - c}{4b}$$

Key observation: $q_1^* = 2 \cdot q_2^*$ — Leader produces twice as much as follower!

Comparing Stackelberg and Cournot Equilibria

Cournot equilibrium (simultaneous moves):

Both firms choose simultaneously, each responding to the other’s expected output.

Equilibrium quantities: $$q_1^C = q_2^C = \frac{a - c}{3b}$$

Stackelberg equilibrium (sequential moves): $$q_1^S = \frac{a - c}{2b}, \quad q_2^S = \frac{a - c}{4b}$$

Comparison:

Key insights:

1. Leader produces more than in Cournot: $q_1^S > q_1^C$
2. Follower produces less than in Cournot: $q_2^S < q_2^C$
3. Total output is higher in Stackelberg: $Q^S > Q^C$
4. Leader earns more profit than in Cournot: $\pi_1^S > \pi_1^C$
5. Follower earns less profit than in Cournot: $\pi_2^S < \pi_2^C$

First-mover advantage: Leader gains at follower’s expense!

Why Does the Leader Benefit?

Strategic commitment: By producing a large quantity first, the leader forces the follower into a difficult position.

Follower’s dilemma:

• If follower produces a lot, market is flooded, price crashes, both lose
• If follower produces little, leader captures most of the market
• Optimal response: Produce less than you would in simultaneous game

Leader’s advantage: By credibly committing to high output, leader induces follower to produce less, leaving more market share for leader.

The commitment must be credible:

• Leader has already invested in production capacity
• Reversing decision is costly
• Follower believes leader’s quantity is fixed

If leader could change their mind after follower responds, the first-mover advantage vanishes!

When First-Mover Advantage Exists

First-mover advantage occurs when:

1. Quantities are strategic substitutes

Increasing your quantity makes opponent want to decrease theirs.

Examples:

• Quantity competition (Stackelberg)
• Capacity investments
• Territorial expansion

2. Commitment is credible

Leader’s decision must be observable and irreversible.

Credible commitments:

• Building factories (physical sunk costs)
• Long-term contracts with suppliers
• Public announcements backed by reputation
• Contractual obligations

Non-credible commitments:

• Cheap talk (“we plan to produce a lot”)
• Easily reversible decisions
• Private information

3. No coordination

If firms can negotiate or collude, first-mover advantage is moot (they’ll just cooperate for joint profit maximization).

4. Follower can observe leader’s move

If follower doesn’t know what leader did, sequential game becomes effectively simultaneous (Cournot).

First-Mover Disadvantage

Sometimes moving first is a disadvantage!

When prices are strategic complements

If your competitor raises prices, you want to raise yours too.

Bertrand competition with differentiated products:

Firms set prices (not quantities), and products are differentiated.

Result: Follower benefits by observing leader’s price and undercutting slightly, or pricing high if leader prices high.

First-mover disadvantage — you reveal information and give competitor flexibility.

When market is uncertain

Moving first means committing before key information is revealed.

Example: Tech product launches

• Leader launches product, may choose wrong features
• Follower observes market response, improves product accordingly
• Fast follower advantage

Real-world:

• Apple wasn’t first in smartphones, but iPhone dominated
• Google wasn’t first in search, but won by observing others’ mistakes
• Facebook wasn’t first in social networking (Friendster, MySpace existed)

When there’s a standard-setting battle

Moving first in standards can be risky if market hasn’t converged.

Example:

• Betamax vs VHS (Sony moved first, lost)
• HD-DVD vs Blu-ray (Toshiba lost to Sony/Blu-ray consortium)

But: In network-effect markets, moving first can also lock in the standard (e.g., QWERTY keyboard, Windows OS).

Real-World Applications

1. Airline Route Entry

Stackelberg model:

• Incumbent airline (leader) sets capacity on a route
• Potential entrant (follower) observes, then decides whether/how much to enter

Leader strategy: Overcapacity — install more seats than optimal for monopoly to deter entry.

Logic:

• Extra capacity is sunk cost
• If entrant enters, leader has high capacity already, floods market
• Low price makes entry unprofitable
• Entrant stays out
• Leader accepts slightly lower monopoly profit to prevent entry

This is a credible threat because capacity is sunk and observable.

2. Pharmaceutical R&D

Leader (first to market):

• Patents protect from direct competition
• High prices during patent period
• First-mover advantage — captures market, builds brand

Follower (generic manufacturers):

• Wait for patent expiration
• Enter with identical product at lower cost
• Fast follower advantage — no R&D costs, proven demand

Result: Innovator gets temporary monopoly, generics get later entry.

3. Platform Competition

Example: Amazon Web Services (AWS)

AWS strategy:

• First to offer comprehensive cloud computing (2006)
• Built massive infrastructure early
• Network effects: More developers → more services → more developers

Followers (Google Cloud, Microsoft Azure):

• Entered years later (2008-2010)
• Better technology in some areas, but smaller ecosystem
• First-mover advantage: AWS has dominant market share

But: Network effects made first-mover advantage very durable here.

4. Union-Firm Bargaining

Stackelberg model: Union (leader) sets wage demand, firm (follower) chooses employment level.

Union’s power: By committing to a wage, union influences firm’s hiring decision.

Outcome: Higher wages, lower employment than simultaneous negotiation.

Entry Deterrence and Strategic Commitments

How can incumbents deter entry?

1. Capacity expansion

Build more capacity than needed for current demand.

Threat: “If you enter, I’ll use all my capacity and crash prices.”

Credibility: Capacity is sunk cost, can’t be undone.

2. Exclusive contracts

Lock up suppliers or distributors with long-term contracts.

Threat: “You can’t get inputs/distribution channels.”

Credibility: Contracts are legally enforceable.

3. Predatory pricing (risky)

Temporarily price below cost to drive out competitors.

Threat: “I can outlast you in a price war.”

Problem: Illegal in many jurisdictions, hard to commit credibly (you lose money too).

4. R&D / Innovation

Continuously improve product to stay ahead.

Threat: “By the time you copy me, I’ll have moved on.”

Credibility: Innovation is hard to reverse, reputational commitment.

The Timing Game: Should You Move First or Second?

Moving first is better when:

• Strategies are strategic substitutes (quantity competition)
• You can make credible commitments
• Network effects or learning curves favor early movers
• Limited market space (land grabs, territory)

Moving second is better when:

• Strategies are strategic complements (price competition)
• Uncertainty about market demand or technology
• You can learn from first mover’s mistakes
• Low imitation costs (easy to copy successful products)

The War of Attrition: Simultaneous Stackelberg

Puzzle: What if both firms want to be the leader?

War of attrition: Both firms delay, hoping the other will commit first (and become the “leader” in a bad sense).

Example: Standards competition

• Each firm wants the other to adopt their standard
• Waiting game ensues
• Market remains fragmented

Result: Potential inefficiency — no one moves, market stagnates.

Solutions:

• Coordination through industry groups
• Government mandates
• One firm makes irreversible investment (becomes de facto leader)

Key Takeaways

1. Stackelberg competition — sequential game where leader moves first, follower responds
2. First-mover advantage — leader produces more and earns higher profit than in simultaneous game
3. Strategic commitment — leader’s advantage comes from credible, irreversible commitment
4. Backward induction — solve follower’s problem first, then leader’s
5. Strategic substitutes — when your action makes opponent want to do less (quantities)
6. First-mover disadvantage — exists in uncertain markets, strategic complements, learning situations
7. Entry deterrence — incumbents use capacity, contracts, innovation to prevent entry
8. Timing matters — optimal strategy depends on market structure, uncertainty, commitment ability

Stackelberg competition shows that the timing of moves is as important as the moves themselves — and that credible commitments can reshape competitive dynamics in your favor.

Practice Problem

Two firms compete in quantities (Cournot-style). Market demand is $P = 100 - Q$ where $Q = q_1 + q_2$. Both firms have marginal cost $c = 10$.

Questions:

1. What are the Cournot equilibrium quantities and profits (simultaneous moves)?
2. What are the Stackelberg equilibrium quantities and profits if Firm 1 moves first?
3. By how much does Firm 1’s profit increase by moving first?

This post is part of the Game Theory Series, where we explore the mathematics of strategic decision-making. Stackelberg competition reveals how the timing of moves and the credibility of commitments shape competitive outcomes.