Module 12.6 Game Theory: Applications to Business Lecture

Game Theory Overview

• Applicable to varied situations, from daily interactions to strategic decision-making in business (e.g. pricing, quality decisions).

• Focus on a duopoly (two firms) vs. a monopoly (one firm).

Example: Pricing Strategies of Two Theaters

• Firms: Premier and Cinemark, both showing the same movies.

• Strategies: Each can set ticket prices at $5 or $10.

• Payoff Matrix:

• Both charge $5 → Each earns $1,000,000 profit.

• Cinemark charges $10 → Premier earns $2,000,000, Cinemark earns $500,000.

• Premier charges $10 → Cinemark earns $2,000,000, Premier earns $500,000.

• Both charge $10 → Each earns $1,500,000.

• Total Profit Analysis:

• Highest total profit occurs at $10 ($3,000,000).

• Prisoner's dilemma structure identified.

Nash Equilibrium

• Cinemark’s Dominant Strategy: Always set price at $5 regardless of Premier’s decision.

• If Premier charges $5: Moving to $10 reduces profit from $1,000,000 to $500,000.

• If Premier charges $10: Moving from $5 to $10 reduces profit from $2,000,000 to $1,500,000.

• Premier’s Dominant Strategy: Same logic applies, leading to Nash Equilibrium at pricing of $5.

• Both firms earn $1,000,000 each.

• Cooperation (collusion) could lead to higher profits ($1,500,000), illustrating competition's consumer benefit.

Collusion and Competition

• Collusion is often illegal and hard to sustain due to prisoner's dilemma conflicts.

• Communication and repetition can help overcome these dilemmas.

Sequential Decision-Making: Quality/Niche Example

• Firms: "Original" (moves first) vs. "Newcomer" (moves second).

• Choices: High-end vs. Discount clothing.

• Payoffs:

• Both high-end → $10,000,000 each.

• Original high-end, Newcomer discount → Original earns $20,000,000, Newcomer earns $12,000,000.

• Original discount, Newcomer high-end → Original earns $12,000,000, Newcomer earns $20,000,000.

• Both discount → $6,000,000 each.

• Backward Induction:

• Newcomer will choose discount if Original occupies high-end (earn $12,000,000 vs. $10,000,000).

• If Original does discount, Newcomer prefers high-end (earning $20,000,000 over $6,000,000).

• Outcome:

• Original produces high-end (earning $20,000,000), Newcomer produces discount (earning $12,000,000).

• Market Dynamics

• Original has a first-mover advantage, influencing Newcomer’s choice.

• Resulting Nash Equilibrium: Original: high-end, Newcomer: discount.

Conclusion

• Game theory applications extend beyond simple examples to complex market scenarios (product differentiation, fixed costs).

• Encourages rigorous decision-making in both personal and business contexts.