Module 6 — Oligopoly, Entry, and Algorithmic Pricing

Cournot, Bertrand, Stackelberg, collusion, entry, platform competition, pricing algorithms, welfare, and competition policy.

Module 6 — Oligopoly, Entry, and Algorithmic Pricing

Core question

How do the strategic variable, timing, product differentiation, capacity, and market rules determine prices, output, entry, and market power?

Learning outcomes

You will be able to:

solve and compare Cournot, Bertrand, and Stackelberg benchmarks;
relate markups to demand elasticity and strategic interaction;
analyse collusion and entry incentives;
diagnose platform power beyond market share alone;
interpret current evidence on algorithmic pricing cautiously.

1. Market structure is a model choice

Feature	Question
strategic variable	quantity, price, capacity, quality, advertising, ranking?
timing	simultaneous, leader–follower, repeated, dynamic entry?
product relation	homogeneous, differentiated, complements, ecosystem?
constraints	capacity, fixed cost, switching, data, compute, regulation?
information	are costs, demand, actions, or algorithm rules observed?

Counting firms is a starting fact, not a complete theory of competition.

For a single-price monopolist with differentiable demand, the first-order condition can be written:

\frac{P-MC}{P}=-\frac1{\varepsilon_D},

where ε_D<0 is the price elasticity at the chosen point. This Lerner relation is a benchmark; multi-product pricing, dynamic demand, regulation, and imperfect measurement complicate empirical markups.

2. Cournot: firms choose quantities

Let inverse demand be:

P=a-bQ,\qquad Q=\sum_iq_i,

with constant marginal cost c. Firm i maximises:

\pi_i=[a-b(q_i+Q_{-i})-c]q_i.

Its best response is:

q_i=\frac{a-c-bQ_{-i}}{2b}

when the expression is positive. With n symmetric firms:

q_i^*=\frac{a-c}{b(n+1)}, \quad Q^*=\frac{n(a-c)}{b(n+1)}, \quad P^*=\frac{a+nc}{n+1}.

Numerical duopoly

Let a=100, b=1, and c=20:

q_1=q_2=\frac{80}{3}\approx26.67,

so Q≈53.33, P≈46.67, and each profit is about £711.11.

As n grows, price approaches marginal cost in this benchmark. Fixed costs and endogenous entry can prevent the number of active firms from growing without bound.

3. Bertrand: firms choose prices

With homogeneous products, constant identical marginal cost, sufficient capacity, and consumers buying from the cheapest seller, any price above c can be undercut. The Nash equilibrium is:

p_1=p_2=c.

This “Bertrand paradox” is not a claim that two real firms always create perfect competition. Relax one assumption:

differentiated products soften price competition;
capacity constraints make undercutting unable to serve the market;
search or switching costs create local power;
repeated interaction can support coordination;
asymmetric costs can leave the efficient firm with a markup.

4. Stackelberg: commitment changes best responses

The leader chooses quantity first and anticipates the follower's Cournot response. In the same numerical market:

q_L=40,\qquad q_F=20,

so Q=60 and P=40. Profits are:

\pi_L=(40-20)40=800, \qquad \pi_F=(40-20)20=400.

Model	Total output	Price	Strategic advantage
monopoly	40	60	coordinated quantity restriction
Cournot duopoly	53.33	46.67	neither moves first
Stackelberg	60	40	leader commits to output
competitive benchmark	80	20	price equals marginal cost

First-mover advantage requires credible commitment. If capacity can be reversed costlessly before rivals react, the Stackelberg logic weakens.

5. Collusion is an incentive problem

A cartel tries to reproduce monopoly output, but each member benefits from secretly expanding while others restrict. Repetition can deter deviation when future punishment is valuable, monitoring is informative, and entry is limited.

Facilitating conditions include:

few symmetric firms and frequent interaction;
transparent prices or quantities;
stable demand and costs;
credible punishment and high entry barriers.

Transparency can help consumers search yet also help firms monitor one another. Its effect is an empirical institutional question.

6. Entry and contestability

Entry occurs when expected post-entry profit covers sunk entry cost. An incumbent may invest in capacity, compatibility, product proliferation, or long contracts before entry.

To distinguish competition from exclusion, ask:

Would the action be profitable without deterring a rival?
Does it lower the incumbent's cost or improve quality?
Does it raise rivals' costs or deny a necessary input?
Is the commitment credible and observable?
What happens to consumers in the short and long run?

Low current prices can reflect competition, predation, penetration pricing, learning, or cross-subsidy. One observation does not identify the mechanism.

7. Platforms and AI foundation models

Platform markets add indirect network effects, multi-homing, data feedback, default placement, interoperability, and often zero monetary prices on one side. Relevant bottlenecks may include compute, chips, cloud distribution, data, app stores, or access to users.

The UK Competition and Markets Authority's 2024 foundation-model update mapped an interconnected set of more than 90 partnerships and investments involving major technology firms and highlighted risks around control of critical inputs and routes to market (CMA, 2024).

This is a forward-looking competition assessment, not a finding that every partnership harms competition. A proper analysis compares efficiencies—funding, compute access, distribution—with foreclosure, dependency, and reduced independent entry.

8. Field evidence on pricing software

Assad, Clark, Ershov, and Xu study Germany's retail gasoline market, where algorithmic-pricing software became widely available. They infer adoption from changes in pricing patterns and instrument with headquarters adoption. Adoption increased margins for non-monopoly stations; in duopoly and triopoly markets, margins rose when all stations adopted (2024).

The evidence is consistent with altered strategic interaction. It does not show that every algorithm autonomously colludes: adoption is inferred, the setting is gasoline retail, and software, market transparency, ownership, and local rivalry matter.

9. Welfare and policy diagnosis

Market power can raise price, reduce quantity, distort quality or innovation, and redistribute surplus. But intervention can also reduce investment or destroy integration efficiencies.

Diagnosis	Candidate response	Main design risk
merger removes close rival	merger control/remedy	wrong counterfactual entry
bottleneck foreclosure	access/interoperability rule	weak security or investment
collusive communication	antitrust enforcement	confusing parallel response with agreement
algorithmic opacity	audit, records, monitoring	box-ticking without causal evidence
switching/data lock-in	portability and open standards	low use or privacy leakage

Practice

Derive the n-firm Cournot equilibrium and its limit as n→∞.
Add a capacity of 20 to each Bertrand firm and explain why p=c may fail.
Compare consumer surplus in monopoly, Cournot, and Stackelberg for the worked market.
Write the one-period deviation condition for cartel cooperation.
Map one AI service from chips to end users and identify two possible bottlenecks and two efficiencies.

Quick check

Oligopoly predictions depend on the strategic variable and timing.
Bertrand's result is powerful because its assumptions are transparent.
Commitment can change equilibrium even when demand and cost do not.
Collusion requires an incentive-compatible punishment path.
Algorithmic adoption evidence is market-specific, not a universal verdict.

Next: analyse hidden types, hidden actions, signals, and contracts.

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Module 5 — Static, Dynamic, and Repeated Games

Best responses, Nash equilibrium, mixed strategies, backward induction, credibility, repeated interaction, and Bayesian games.

Module 7 — Information Economics and Contracts

Adverse selection, signalling, screening, moral hazard, incentive compatibility, and machine-learning credit evidence.