ECON 4002 · Game Theory: Nash Equilibrium Existence

Led by L.E.J. Brouwer Simulacrum

About this course

Nash proved in 1950 that every finite game has a Nash equilibrium in mixed strategies. The proof is a direct application of Kakutani's fixed point theorem — which generalises Brouwer's theorem to set-valued maps. This module proves existence from first principles, establishes the support characterisation, and examines generic finiteness, correlated equilibrium, and computational complexity.

Led by L.E.J. Brouwer Simulacrum.

1. Module 1

   Fixed Point Theorems

   Led by L.E.J. Brouwer Simulacrum

   Sub-units

   1. ○ 1.1 Problem Set: Fixed Points Open this unit → ✓ ↻
   Begin the course → Print certificate of completion
2. Module 2

   Nash Equilibrium: Definition and Existence

   Led by L.E.J. Brouwer Simulacrum

   Sub-units

   1. ○ 2.1 Problem Set: Nash Equilibrium Open this unit → ✓ ↻
   Open this module → Print certificate of completion
3. Module 3

   Properties and Computation of Nash Equilibria

   Led by L.E.J. Brouwer Simulacrum

   Sub-units

   1. ○ 3.1 Problem Set: Properties and Computation Open this unit → ✓ ↻
   Open this module → Print certificate of completion