Oligopoly, Game Theory & Competition Policy

Learning Objectives

  • Identify market structures between monopoly and perfect competition.
  • Analyze possible outcomes in oligopoly markets.
  • Understand the prisoner’s dilemma and its relevance to oligopoly.
  • Examine how competition laws foster competition in oligopolistic markets.

Key Features of Oligopoly

  • Few sellers → each firm’s output & price decisions affect rivals’ profits.
  • Strategic interdependence ⇒ requires game-theoretic analysis.
  • Tension between cooperation ( cartel–like monopoly outcome ) and self-interest ( competitive outcome ).
  • Examples in Canada: hockey skates (Nike–Bauer vs. Reebok–CCM), airlines (WestJet vs. Air Canada).

Fundamental Concepts & Definitions

  • Game theory: Study of behavior in strategic situations.
  • Duopoly: Oligopoly with exactly two firms.
  • Collusion: Agreement on quantities or prices.
  • Cartel: Group of firms acting as a single monopolist.
  • Nash equilibrium (NE): Each actor chooses best strategy given rivals’ chosen strategies.
  • Dominant strategy: Best regardless of rivals’ moves.
  • Prisoner’s dilemma (PD): Game illustrating why mutually beneficial cooperation can fail.

Duopoly Water Example (Jack & Jill)

Market data (marginal cost =0)

  • Demand schedule (excerpt):
    • Q=60 \text{ L} \Rightarrow P=60\, ⇒ TR=3{,}600.
    • Q=120 \text{ L} \Rightarrow P=0\, ⇒ competitive outcome.

Benchmarks

  • Perfect competition: P=MC=0, Q=120 \text{ L}.
  • Monopoly ( or successful cartel ): Q=60, P=60, \pi_{total}=3{,}600.
  • If cartel split equally ⇒ each firm: q=30, \pi=1{,}800.

Non-cooperative Nash Equilibrium

  • Reasoning: Given rival produces 30, increasing own output to 40 raises individual profit from 1{,}800 to 2{,}000 despite lowering total profit.
  • Symmetric incentives produce q{Jack}=q{Jill}=40 ⇒ Q=80, P=40, each \pi=1{,}600.
  • Outcomes hierarchy:
    • Q{NE}=80 > Q{Monopoly}=60 > Q_{Cartel\ agreement}.
    • P{NE}=40 < P{Monopoly}=60 but > P_{Competitive}=0.

General Result

Q{competition} > Q{oligopoly\;NE} > Q{monopoly} P{competition} < P{oligopoly\;NE} < P{monopoly}

Effect of Oligopoly Size

  • Output effect: Selling one more unit at P>MC raises profit.
  • Price effect: Raising total output lowers P on all units ⇒ lowers profit.
  • As number of firms ↑, individual price effect ↓ → NE approaches perfect competition.
  • Insight: International trade increases number of sellers globally ⇒ market behaves more competitively (e.g., auto industry with Toyota, Honda, VW, BMW, Ford, GM).

The Prisoner’s Dilemma (PD)

Canonical Story (Bonnie & Clyde)

  • Payoff matrix (years in jail):
    • Both silent ⇒ (1,1).
    • Both confess ⇒ (8,8) (NE, dominant strategy).
    • One confesses, other silent ⇒ (0,20)$ or $(20,0)$.
  • Dominant strategy: Confess.
  • Lesson: Rational self-interest leads to sub-optimal joint outcome.

Mapping PD to Oligopoly

  • Jack & Jill’s production game mirrors PD: low output (30 L) vs. high output (40 L).
  • High–high (40 L,40 L) = NE analogous to confess–confess.

Additional PD Applications

  • OPEC: Coordinated quotas vs. cheating (historical price swings \$3 \rightarrow \$35 \rightarrow \$13 per barrel).
  • Advertising rivalry (Molson vs. Labatt): advertising = dominant strategy, joint profits ↓.
  • Common-resource overuse (Shell vs. Esso drilling wells) ⇒ excessive wells, pure waste.

Repeated Games & Cooperation

  • Threat of future punishment (e.g., “grim trigger” or tit-for-tat strategy) can sustain cooperation when \text{PV of future loss} > \text{current gain}.
  • Tit-for-tat algorithm: start cooperative, then mimic opponent’s previous move → proven winner in Axelrod’s tournament.

Public Policy Toward Oligopolies

Canadian Competition Act (selected §45(1))

  • Criminalizes agreements that “limit, prevent, lessen unduly” production, facilities, competition, or raise prices.
  • Penalties: up to 5 years imprisonment and/or \$10 \text{ million} fine per offence.
  • Enforcement bodies: Competition Bureau (investigation) → Attorney General (criminal) or Competition Tribunal (civil).
  • Other criminal provisions: bid-rigging, price discrimination, resale price maintenance, predatory pricing.

Controversial Practices

  1. Resale Price Maintenance (RPM)

    • Supplier sets minimum resale price P_{min}.
    • Critics: Restricts retailer price competition.
    • Defenders: Solves free-rider problem on retail services; if goal were monopoly power, supplier could just raise wholesale price.

  2. Predatory Pricing

    • Incumbent sets P<MC intending to drive rival out then recoup losses.
    • Economists skeptical: costly for predator; rival can temporarily contract; evidence rare.

  3. Tying (Bundling)

    • Selling goods A & B together (e.g., blockbuster + art film).
    • Simple monopoly-extension argument weak: willingness-to-pay unchanged.
    • Can be price discrimination when customers value goods differently.
    • Ambiguous welfare impact ⇒ legal debate continues.

Recent Canadian Case: Bread Price-Fixing

  • Major grocers & bakeries (Loblaw, Walmart, Sobeys, Metro, Giant Tiger, Canada Bread) alleged to have fixed bread prices for 14 years.
  • Penalties: up to 20\% of affected sales, \le \$25\,\text{m}/count + imprisonment.
  • Loblaw received immunity (whistle-blower) & issued \$25 gift cards.
  • Societal impact: Bread prices ↑ 5.25\%/yr vs. food inflation 2.57\% (2002-2014).

Quick Quiz Key Takeaways

  1. Key oligopoly feature: small number of strategically interacting firms.
  2. Cooperative cartel output < competitive level; = monopoly level.
  3. Non-cooperative oligopoly output > monopoly; < competitive.
  4. As firms ↑, industry output → competitive level.
  5. PD shows rational self-interest may block mutually beneficial cooperation.
  6. Repeated interaction & credible retaliation promote cooperation.
  7. Competition (antitrust) laws aim to prevent firms from reducing competition.
  8. Enforcement controversial because some practices that look anticompetitive may have efficiency motives.

Mathematical & Numerical Highlights

  • Profit under zero MC: \pi=TR=PQ.
  • Output vs. price effect balancing condition: increase output until \Delta \pi{output}=\Delta \pi{price}.
  • Present value condition for maintaining cooperation in repeated games: G < \frac{\delta L}{1-\delta} where G = one-time gain from cheating, L = per-period loss from punishment, \delta = discount factor.

Chapter in a Nutshell (Official Summary)

  • Oligopolists prefer cartel outcome but self-interest pushes towards competitive outcome; position depends on number of firms & ability to cooperate.
  • PD framework explains failures of cooperation across many contexts.
  • Anticompetition laws seek to curb cooperative behavior that harms welfare, yet must distinguish harmful from efficiency-enhancing practices.

Connections & Implications

  • Links to Chapter 7 (efficiency & deadweight loss): Non-cooperative oligopoly often closer to efficient surplus-maximizing outcome than collusion.
  • Links to Chapter 3 (comparative advantage): Trade enlarges the “number of firms,” fostering competition.
  • Ethical issues: balancing consumer welfare vs. firm profits; prison sentences for white-collar crimes.
  • Real-world relevance: OPEC, airline fare wars, national ad bans, salary caps in sports, doping in athletics.

Formulas & Equations Summary (LaTeX)

  • Monopoly optimal MR=MC ⇒ with linear demand P(Q)=a-bQ, MR=a-2bQ.
  • Cournot duopoly NE (symmetric, constant MC=0): Qi=\frac{a}{3b} ⇒ Q{total}=\frac{2a}{3b}, P=\frac{a}{3}.
  • Competitive output: Q_{PC}=\frac{a}{b}, P=MC.
  • Deadweight loss under oligopoly: area between P{oligopoly} and MC over units Q{social}-Q_{oligopoly}$$.