Game Theory

Game theory is the study of mathematical models of strategic interaction among rational decision-makers, providing a framework for analyzing situations where the outcome for one "player" depends not only on their own actions but also on the actions of others. As a foundational tool in economics, it is used to understand behavior in contexts like oligopolies, auctions, bargaining, and public goods, by analyzing the strategies, payoffs, and information available to each participant. The goal is often to identify an equilibrium, such as the famous Nash Equilibrium, which represents a state where no player can benefit by unilaterally changing their strategy, thus offering predictions about the results of competitive or cooperative interactions.

1. Introduction to Game Theory
   1. Defining Game Theory
      1. Formal Definition
      2. Mathematical Framework
      3. Strategic Interaction
      4. Decision-Making Under Interdependence
   2. Key Features of Games
      1. Strategic Interdependence
      2. Rational Decision-Making
      3. Outcome Dependence on All Players
      4. Rule-Based Structure
   3. Core Assumptions
      1. Rationality of Players
         1. Utility Maximization
         2. Consistency of Preferences
         3. Transitivity of Preferences
         4. Completeness of Preferences
      2. Common Knowledge
         1. Shared Understanding of Game Structure
         2. Knowledge of Rationality
         3. Knowledge of Payoffs
         4. Knowledge of Available Strategies
   4. Historical Development
      1. Early Origins
         1. Mathematical Foundations
         2. Economic Motivations
      2. Foundational Contributors
         1. John von Neumann
         2. Oskar Morgenstern
         3. Theory of Games and Economic Behavior
      3. Modern Development
         1. John Nash
         2. Nash Equilibrium Concept
         3. Nobel Prize Recognition
      4. Contemporary Extensions
         1. Mechanism Design
         2. Evolutionary Game Theory
         3. Behavioral Game Theory
   5. Scope and Applications
      1. Economics and Finance
      2. Political Science and International Relations
      3. Biology and Evolution
      4. Computer Science and AI
      5. Psychology and Sociology
      6. Business Strategy and Management