Overview
This lecture applies the prisoner's dilemma to the Coke and Pepsi oligopoly, examines dominant strategies and Nash equilibrium, and discusses how the dilemma can be overcome using real-world tactics like tacit collusion and price match guarantees.
Oligopoly and the Prisoner's Dilemma
- Coke and Pepsi are the major competitors in an oligopoly market.
- Both firms make more profit if both charge high prices ($1,000 each).
- If both charge low prices, each earns less ($400 each).
- If one charges a high price and the other a low price, the low-price firm earns more ($1,500), and the high-price firm earns less ($200).
Dominant Strategies and Nash Equilibrium
- Each firm's dominant strategy is to charge a low price, regardless of the competitor’s choice.
- When both follow their dominant strategy (low price), they reach a Nash equilibrium with lower profits ($400 each).
- This outcome mirrors the prisoner's dilemma, where mutual cooperation (high price) would yield better results, but rational self-interest leads to a worse collective outcome.
Beating the Prisoner’s Dilemma
- Collusion (explicit agreement on high prices) is illegal but hard to prove if firms independently choose high prices.
- Tacit agreements or mutual understanding can lead both firms to charge high prices without direct collusion.
- Cheating by undercutting is tempting but less beneficial if the game is repeated over time, as long-term cooperation yields higher cumulative profits.
- Repeated interactions (daily profits) incentivize long-term cooperation over one-time gains from cheating.
Price Match Guarantees
- A price match guarantee removes the incentive to undercut because any lower price is immediately matched.
- The payoff matrix changes: high price by both yields $1,000 each; any low price by one triggers both to receive $400 each.
- Nash equilibrium shifts to both charging high prices.
- Studies show firms with price match guarantees tend to charge higher prices, as these guarantees segment the market and raise average prices.
Key Terms & Definitions
- Oligopoly — a market structure dominated by a few firms.
- Prisoner's Dilemma — a situation where individual rational choices lead to a worse collective outcome.
- Dominant Strategy — an action that results in the highest payoff regardless of what the other player does.
- Nash Equilibrium — a set of strategies where no player can improve their outcome by changing their own strategy.
- Tacit Collusion — informal agreement between firms to avoid competitive pricing without explicit communication.
- Price Match Guarantee — a promise to match competitors’ prices, often resulting in higher overall prices.
Action Items / Next Steps
- Review the payoff matrix examples and understand dominant strategy rationale.
- Prepare for the next class by considering how other game theory scenarios differ from the prisoner's dilemma.