Game Theory

1. Game Solutions
   1. Nash Equilibrium
      1. Definition and Intuition
         1. Explanation of concept
         2. Importance in predicting game outcomes
      2. Existence
         1. Conditions for existence
         2. Brouwer's Fixed Point Theorem
      3. Uniqueness
         1. Conditions under which Nash equilibrium is unique
         2. Implications of multiple equilibria
      4. Mixed Strategies
         1. Definition of mixed strategies
         2. Application in games with no pure strategy equilibrium
      5. Mixed Nash Equilibrium
         1. Explanation and significance
         2. Calculating mixed equilibria
   2. Dominant Strategy Equilibrium
      1. Definition and Understanding
         1. Concept of dominant strategy
         2. Implications of dominant strategies in games
      2. Existence and Identification
         1. How to identify dominant strategy equilibria
         2. Examples of games with dominant strategies
   3. Pareto Efficiency
      1. Concept of Pareto Optimality
         1. Definition of Pareto efficient outcomes
         2. Relation to social welfare
      2. Pareto Efficiency in Games
         1. Identifying Pareto optimal outcomes
         2. Use in cooperative and non-cooperative contexts
   4. Subgame Perfect Equilibrium
      1. Understanding Sequential Games
         1. Definition and importance of extensive forms
         2. Identifying subgames
      2. Definition and Calculation
         1. Backward induction process
         2. Importance in perfect information games
   5. Bayesian Nash Equilibrium
      1. Games with Incomplete Information
         1. Definition and challenges
         2. Types of information asymmetries
      2. Bayesian Games
         1. Representation of beliefs and types
         2. Role of Bayes' rule in deriving equilibria
         3. Applications in economic and strategic settings