Game Theory

Fundamentals and Strategic Decision Making

🎯
🤝
📊

Understanding the Mathematics of Conflict and Cooperation

What is Game Theory?

Game theory is the mathematical study of strategic decision-making among rational individuals or entities called "players."

Game
Players
Strategies
Payoffs
Information
Rules
Outcomes

Key Components:

Players: Decision-makers in the game
Strategies: Available actions or choices
Payoffs: Outcomes or rewards
Information: What each player knows

Real-World Applications:

Economics, politics, biology, psychology, military strategy, business competition, auction design, and social interactions.

Cooperative vs Non-Cooperative Games

Player A
Player B

🤝 Cooperative Games

  • Players can form binding agreements
  • Communication and coordination allowed
  • Focus on coalition formation
  • Enforceable contracts

⚔️ Non-Cooperative Games

  • No binding agreements possible
  • Players act independently
  • Focus on individual strategies
  • Self-enforcing equilibria

Examples:

Cooperative: International climate agreements, business partnerships, labor unions

Non-Cooperative: Prisoner's Dilemma, market competition, voting systems

Zero-Sum vs Non-Zero-Sum Games

⚖️ Zero-Sum Games

  • One player's gain = another's loss
  • Total payoff always equals zero
  • Pure competition
  • No mutual benefit possible

🎯 Non-Zero-Sum Games

  • Players can both win or both lose
  • Total payoff can be positive or negative
  • Cooperation can be beneficial
  • Win-win outcomes possible

Example: Prisoner's Dilemma (Non-Zero-Sum)

Player 2: Cooperate Player 2: Defect
Player 1: Cooperate (3, 3) (0, 5)
Player 1: Defect (5, 0) (1, 1)
Click on any cell to highlight payoffs

Types of Games: Timing and Information

Turn-Based vs Real-Time Games

Player 1 Moves
→
Player 2 Observes
→
Player 2 Moves

Sequential Game Flow

🏃 Turn-Based (Sequential)

  • Players move in a specific order
  • Each player observes previous moves
  • Strategic advantage to timing
  • Examples: Chess, negotiations

⚡ Real-Time (Simultaneous)

  • All players choose simultaneously
  • No knowledge of others' choices
  • Strategic uncertainty
  • Examples: Auction bidding, pricing

Strategic Implications:

Sequential games often involve backward induction and commitment strategies.

Simultaneous games require predicting opponents' likely actions without direct information.

Deterministic vs Stochastic Games

Uncertainty Level in Games

Deterministic Stochastic
Uncertainty Level: 50%

🎲 Deterministic Games

  • No random elements
  • Outcomes fully determined by strategies
  • Perfect predictability given actions
  • Complete information possible

🎰 Stochastic Games

  • Random elements influence outcomes
  • Probability distributions over payoffs
  • Expected value calculations
  • Uncertainty in results

Examples and Applications:

Deterministic: Tic-tac-toe, contract negotiations
Stochastic: Poker, insurance markets, financial trading

Key Insight:

Stochastic games require players to think in terms of expected payoffs and risk management, while deterministic games allow for precise strategic calculations.

Summary and Real-World Applications

🤝⚔️
Cooperation vs Competition

Whether binding agreements are possible

⚖️🎯
Zero-sum vs Non-zero-sum

Whether mutual benefit exists

🏃⚡
Sequential vs Simultaneous

Timing of decision-making

🎲🎰
Deterministic vs Stochastic

Role of uncertainty

Applications Across Disciplines:

Next Steps in Game Theory:

Nash equilibria, dominant strategies, evolutionary stability, mechanism design, and behavioral game theory.

1 / 7