Econ Chapter 18

Introduction to Oligopoly

• Key idea: Oligopoly = market structure with only a few sellers whose decisions are interdependent.
  • Strategic interactions matter → requires game theory.
  • Contrast with
  • Perfect competition / monopolistic competition → firms so small that strategic effects ≈ 0.
  • Monopoly → only one seller, so no strategic rival to consider.
• Example (tennis balls): Penn, Wilson, Dunlop, Prince, Babolat dominate U.S. market; price & quantity depend on joint behavior.
• Strategic situations: Chess, checkers, business pricing, capacity, advertising, R&D, etc.

18-1. Markets with Only a Few Sellers

• Cooperation vs. self-interest tension
  • Jointly, firms can mimic a monopoly → restrict output, raise price, earn monopoly profit.
  • Individually, each firm has an incentive to cheat to increase own profit.

18-1a. A Duopoly Example (Jack & Jill Water Wells)

• Two firms (duopoly) pumping water at zero MC=0.
• Demand schedule (selected points):
  • Q=10\Rightarrow P=\$110, TR=\$1{,}100
  • Q=60\Rightarrow P=\$60, TR=\$3{,}600 (monopoly quantity)
  • Q=80\Rightarrow P=\$40, TR=\$3{,}200 (Nash equilibrium quantity)
• Monopoly outcome:
  • Cooperative cartel chooses QM=60\text{ gallons} → PM=\$60.
  • Each produces 30 gallons, profit per firm =30\times 60=\$1{,}800, total =\$3{,}600.
• Incentive to cheat: If Jill sticks to 30, Jack can raise to 40 → total 70, P=\$50, Jack’s profit =40\times50=\$2{,}000.
• Mutual cheating → Nash Equilibrium (NE):
  • Each produces 40, total 80, P=\$40.
  • Profit per firm =40\times40=\$1{,}600 (lower than cartel, higher output, lower price).
• Summary principle:
  • Q{NE}>Q{Monopoly}>Q_{Perfect\;Comp}
  • P{NE}

18-1c. Definition of Nash Equilibrium

• A set of strategies where each player’s choice is optimal given the other players’ choices.
• No unilateral incentive to deviate.

18-1d. Size of Oligopoly & Market Outcome

• Marginal analysis for each firm:
  • Output effect: Selling +1 unit raises revenue by P>MC → positive.
  • Price effect: Increasing total Q lowers P on all units → negative.
• As number of firms (n) rises → individual market share ↓ → price effect ↓ → firms behave more competitively.
  • Limit as n\to\infty → price → MC, output → socially efficient level.
• Trade link: International trade increases number of producers globally, pushing outcomes closer to competition.

18-2. The Economics of Cooperation

• Game theory tool: Prisoners’ Dilemma (PD).

18-2a. The Prisoners’ Dilemma Story (Bonnie & Clyde)

• Payoff matrix (sentences):
  • Both silent → 1 yr each (best joint).
  • Both confess → 8 yrs each (NE).
  • One confesses, other silent → confessor 0 yrs, silent 20 yrs.
• Dominant strategy = confess for each.
• Shows non-cooperative equilibrium worse for both vs. cooperation.

18-2b. Oligopolies as a Prisoners’ Dilemma

• Jack & Jill payoff matrix mirrors PD (profits instead of jail time).
  • Dominant strategy = high production (40).
  • Cooperative low production (30) unstable.
• Real-world analogue: OPEC Plus oil cartel.
  • 1973-85 high cooperation → price from \$3 to \$35/bbl.
  • Cheating & new tech (fracking) → price fall, lower cartel power.

18-2c. Other PD Examples

1. Arms Races (U.S. vs USSR/China):
   • Dominant strategy = arm ⇒ both at risk.
   • Arms-control treaties attempt to enforce cooperation.
2. Common-Resource Overuse (ExxonMobil vs Chevron pool):
   • Each can drill one or two wells.
   • Dominant = two wells; outcome wastes resource (profits $40M each vs $50M with cooperation).

18-2d. Welfare Implications

• If cooperation ↑ total surplus (arms race, commons) → society wants cooperation.
• If cooperation ↓ total surplus (price-fixing oligopoly) → society benefits from lack of cooperation.
• Police interrogation: society benefits when suspects don’t cooperate.

18-2e.