Lecture 4 - Characteristics and Applications of Nash Equilibrium

03.11

Instructor: Yaodong Yang

Topics Covered

1. The Meaning of Nash Equilibrium
   • 1.1 Example: Chicken Game
2. Existence of Nash Equilibrium
   • 2.1 Best Response Correspondence
   • 2.2 Kakutani Fixed Point Theorem
   • 2.3 Sperner’s Lemma
   • 2.4 Proof of Existence
   • 2.5 PPAD-Completeness
   • 2.6 Approximation Algorithms
     • 2.6.1 TS Algorithm
     • 2.6.2 Approximation Results: 0.3393, 1/3
3. Multiplicity of Nash Equilibria
   • 3.1 Example: Chicken Game
   • 3.2 Equilibrium Refinement
     • 3.2.1 Focal Point Effect
     • 3.2.2 Example: The Battle of the Sexes
   • 3.3 Cheap Talk
     • 3.3.1 Definition
     • 3.3.2 Example: The Battle of the Sexes
   • 3.4 Correlated Equilibrium
     • 3.4.1 Definition
     • 3.4.2 Example: The Battle of the Sexes
     • 3.4.3 Example: Dice Tossing
   • 3.5 Comparison: Correlated Equilibrium vs. Nash Equilibrium