Lesson 8.2 · 25 of 25 lessons
Game equilibrium
Use constraint vertices and payoff matrices to explore optimization applications.
Open the interactive animation01 · Story
What to verify in this scene
Follow the explanations and operations, then identify the mathematical evidence that remains in the final scene.
- 01
G records the payoff for each pair of strategies
- 02
Multiply G by mixed strategy p, which assigns equal probability to both choices
- 03
payoff is the zero vector, favoring neither pure strategy
A mixed strategy creates an unexploitable balance
02 · Notebook
The runnable notebook
This source creates the mathematical objects and controls the order of operations and animation. Read it here, then play the same scene yourself.
2d
zoom 1
coordinates on
1 -1 #G
-1 1
// {{G}} records the payoff for each pair of strategies
checkpoint Game equilibrium
1/2, 1/2 #p@
// Multiply {{G}} by mixed strategy {{p}}, which assigns equal probability to both choices
G * p #payoff@
// {{payoff}} is the zero vector, favoring neither pure strategy\nA mixed strategy creates an unexploitable **balance**
focus payoff03 · Unit 8
Lessons in this unit
Linear programming & game theory — Use constraint vertices and payoff matrices to explore optimization applications.