Unit 2515: Introduction to Game Theory

1. Introduction to Game Theory

• Definition of a game
• Players: participants and their roles
• Strategies: possible actions
• Payoffs: outcomes and utilities
• Importance and applications of game theory

2. Types of Games

• Simultaneous Games: players choose strategies without knowledge of others’ choices
• Sequential Games: players make moves in sequence, with knowledge of earlier actions
• Cooperative Games: players can form binding agreements
• Non-Cooperative Games: no enforceable agreements
• Zero-Sum Games: one player’s gain equals another’s loss
• Non-Zero-Sum Games: outcomes can be mutually beneficial or harmful

3. Nash Equilibrium

• Definition and intuition
• Formal mathematical description
• Existence of Nash equilibria
• Examples in different game types
• Significance in predicting outcomes

4. Prisoner's Dilemma

• Description of the scenario
• Payoff matrix analysis
• Implications for cooperation and trust
• Real-world analogues and lessons

5. Mixed Strategies

• Concept of randomizing strategies
• When pure strategies fail
• Calculating mixed strategy equilibria
• Examples and applications

6. Extensive Form Games

• Game trees and representation
• Nodes, branches, and payoffs
• Information sets and imperfect information
• Backward induction method
• Examples of sequential decision-making

7. Dominant Strategies

• Definition and identification
• Dominant vs dominated strategies
• Role in simplifying game analysis
• Examples illustrating dominant strategies

8. Game Theory Applications

• Economics: market competition, auctions
• Business: negotiation, pricing strategies
• Political Science: voting, bargaining
• Biology: evolutionary strategies, animal behavior
• Other domains: computer science, sociology

9. Behavioral Game Theory

• Incorporation of psychological factors
• Deviations from purely rational behavior
• Experimental findings and models
• Concepts like fairness, trust, and bounded rationality

10. Evolutionary Game Theory

• Basics of evolutionary dynamics
• Replicator equations
• Evolution of strategies over time
• Applications in biology, sociology, and economics
• Stability concepts (evolutionarily stable strategies)