Discussion

• Normal Form Games
  • Motivating example: Coordination Game
  • Definition of Normal Form Game
  • Definition of a Zero Sum Game
  • Examples of other Normal Form Games
  • Using Nashpy
• Strategies
  • Motivating example: Strategy for Rock Paper Scissors
  • Definition of a strategy in a normal form game
  • Definition of support of a strategy
  • Strategy spaces for Normal form Games
  • Calculation of expected utilities
  • Linear algebraic calculation of expected utilities
  • Using Nashpy
• Best responses
  • Motivating example: Best Responses in Matching Pennies
  • Definition of a best response in a normal form game
  • Generic best responses in 2 by 2 games
  • General condition for a best response
  • Definition of Nash equilibrium
  • Using Nashpy
• Support enumeration
  • Motivating example: Coordination Game
  • The support enumeration algorithm
  • Using Nashpy
• Vertex enumeration
  • Discussion
• Extensive Form Games
  • Motivating example: A modification of the Coordination Game
  • Definition of an Extensive Form Game
  • Imperfect information
  • Definition of an information set
  • Definition of a strategy in an extensive form game
  • Equivalence of Extensive and Normal Form Games
  • Using Nashpy
• Repeated Games
  • Motivating example: Repeated Coordination Game
  • Definition of a repeated games
  • Strategies in a repeated game
  • Equilibria in repeated games
  • Using Nashpy
• The Lemke Howson Algorithm
  • Discussion
• Degenerate games
• Fictitious play
  • Discussion
• Stochastic fictitious play
  • Discussion
• Replicator dynamics
  • Discussion
• Asymmetric replicator dynamics
  • Discussion