What is Game Theory and Decision Analysis?
Game theory is a mathematical framework for analyzing strategic interactions where each player's outcome depends on their choice and others' choices. It's used to study competition, negotiation, cooperation, and rational decision-making in business, economics, and beyond. Understanding game theory helps predict behavior and design better strategies.
Game theory finds optimal strategies using concepts like Nash equilibrium (no player benefits from unilateral change) and identifies dominant strategies. It models payoffs (outcomes) for each combination of player choices, revealing which strategies are rational and stable.
- •Best choice regardless of what others do
- •Always optimal, always rational to use
- •May not be efficient for all players
- •Example: Prisoner's Dilemma (both confess)
- •No player benefits from unilateral change
- •Both players playing their best response
- •Stable but may not be optimal
- •Example: Price competition reaches equilibrium
Step-by-step worked examples
Two companies in a duopoly pricing game. Both can charge High or Low. High yields $10M each if both charge High; $5M if one High, one Low; $2M each if both Low. What is the Nash equilibrium?
If B charges High: A earns $10M (High) vs $5M (Low) → A prefers High If B charges Low: A earns $5M (High) vs $2M (Low) → A prefers High Same logic for B: always prefers High Nash equilibrium: Both charge High (each earns $10M) NOTE: Collusion (both stay High) requires enforcement; without it, both have incentive to deviate.
A software company (Firm A) wants to enter a market where Microsoft dominates. Should A match Microsoft's pricing or undercut?
If A matches: Both profitable but slow growth for A; Microsoft may cut price or bundle features If A undercuts: Microsoft cuts price harder → price war, both lose profitability Game-theoretic insight: Price war is a negative-sum game for both Better strategy: Differentiate on features, target a niche, avoid direct price competition Dominant strategy = differentiate, not compete on price alone.
Prisoner's Dilemma: Two suspects arrested. Each can Confess or Stay Silent. Confess: 3 years if partner silent, 2 if both confess. Silent: 5 years if partner confesses, 1 if both silent. What happens?
From each suspect's view: Confessing yields 3 or 2 years; Staying Silent yields 5 or 1 year Rational choice for each: Confess (dominates staying silent) Nash equilibrium: Both confess → 2 years each Paradox: Both would prefer staying silent (1 year each), but individually rationally choose confessing Lesson: Individual rationality ≠ collective optimality. Trust and enforcement break the dilemma.
Flashcards
Quick quiz
Q1.In a price-setting game, both firms charge $100 and earn $50M. One firm cuts to $90 and earns $60M; the other falls to $40M. This is NOT a Nash equilibrium because:
Q2.Game theory predicts that without enforcement, cartels (price-fixing agreements) are:
Q3.A company offers a discount to early customers. This is a strategic move to:
Q4.When two firms cooperate instead of competing, the outcome is:
The full card deck, worked steps and AI-tutor support for “What is Game Theory and Decision Analysis?” are in Notek — study by hand before your exam.
Common mistakes
Assuming rational players always maximize their own payoff without considering others' responses. — Correct: Rational players anticipate others' moves. Strategy involves predicting others' best responses and choosing accordingly.
Thinking Nash equilibrium is always the best outcome for players. — Correct: Nash equilibrium is stable but may be inefficient (Prisoner's Dilemma). Cooperation often beats Nash equilibrium.
Confusing dominant strategy with Nash equilibrium. — Correct: Dominant strategy is always best regardless of others; Nash equilibrium is stable but depends on others' choices.
Assuming one-time games. Ignoring that repeated games change incentives. — Correct: Repeated games allow reputation, trust, and punishment. Strategies that fail once may succeed when played repeatedly.
FAQ
What is game theory used for in business?
Predicting competitor behavior, setting optimal prices, deciding on product features, negotiating deals, and designing contracts. It reveals which strategies are stable and profitable.
Is game theory always realistic?
Game theory assumes rational players with perfect information. Real players have biases and incomplete info. Use it as a framework, not a perfect predictor.
Can cooperation beat competition in game theory?
Yes, when games are repeated and reputation matters. One-time games favor individual defection; repeated games reward cooperation.
What is a zero-sum game?
A game where one player's gain is another's loss (e.g., chess, poker). Most business games are non-zero-sum (both can win or lose).