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 $q<em>{Jack}=q</em>{Jill}=40$ ⇒ $Q=80$, $P=40$, each $\pi=1{,}600$.
• Outcomes hierarchy:
  • Q{NE}=80 > Q{Monopoly}=60 > Q_{Cartel\ agreement}.
  • $P<em>{NE}=40 < P</em>{Monopoly}=60$ 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}$$.