Game Theory

1. Types of Games
   1. Cooperative vs. Non-Cooperative Games
      1. Cooperative Games
         1. Definition and Characteristics
            1. Focus on group strategies and joint actions
            2. Binding agreements possible
         2. Coalition Formation
            1. Concept of coalitions or alliances
            2. Core, Shapley Value, and Nucleolus
         3. Examples
            1. Team sports strategies
            2. Joint ventures in business
      2. Non-Cooperative Games
         1. Definition and Characteristics
            1. Individual strategy optimization
            2. No binding agreements enforced
         2. Equilibrium Concepts
            1. Nash equilibrium
            2. Dominant strategies
         3. Examples
            1. Competitive business environments
            2. R&D competition in technology
   2. Symmetric vs. Asymmetric Games
      1. Symmetric Games
         1. Definition and Characteristics
            1. Players have identical strategies and payoffs
            2. Any change in perceptions equally affects all players
         2. Examples
            1. Rock-paper-scissors
            2. Battle of the sexes with equal roles
      2. Asymmetric Games
         1. Definition and Characteristics
            1. Different strategies or payoffs for players
            2. Role-specific advantages or disadvantages
         2. Examples
            1. Chess, where players have unique starting positions
            2. Predator-prey interactions in biology
   3. Zero-Sum vs. Non-Zero-Sum Games
      1. Zero-Sum Games
         1. Definition and Characteristics
            1. One player's gain is exactly balanced by the losses of others
            2. Total utility remains constant
         2. Examples
            1. Poker
            2. Competitive sports where one winner is declared
      2. Non-Zero-Sum Games
         1. Definition and Characteristics
            1. Players’ interests can overlap; gains and losses aren't rigidly opposed
            2. Potential for mutually beneficial outcomes
         2. Examples
            1. Trade negotiations
            2. Environmental policy agreements
   4. Simultaneous vs. Sequential Games
      1. Simultaneous Games
         1. Definition and Characteristics
            1. All players make their moves without knowledge of others' actions
            2. Typically modeled with payoff matrices
         2. Examples
            1. Rock-paper-scissors
            2. Certain marketing decisions where competitive actions are simultaneous
      2. Sequential Games
         1. Definition and Characteristics
            1. Players make decisions one after another, with previous actions visible
            2. Often represented by game trees
         2. Examples
            1. Chess or Go
            2. Investment decisions when a firm's choice influences the industry's response
   5. Perfect Information vs. Imperfect Information Games
      1. Perfect Information Games
         1. Definition and Characteristics
            1. All players have complete knowledge of all preceding events and moves
            2. No hidden information or uncertainty
         2. Examples
            1. Chess
            2. Tic-tac-toe
      2. Imperfect Information Games
         1. Definition and Characteristics
            1. Players lack full visibility of previous actions or game state
            2. Often involves probabilistic strategies
         2. Examples
            1. Poker, where opponents' cards are unknown
            2. Battleship, where opponent's board positions are unknown