SLIDE 1
CS214:presentation Zero-sum Game & von Neumann minimax theorem
Group:Second++
What is a Game
Stone Scissors Paper Stone 0,0 +1,-1
- 1,+1
Scissors
- 1,+1
0,0 +1,-1 Paper +1,-1
- 1,+1
CS214:presentation Zero-sum Game & von Neumann minimax theorem - - PowerPoint PPT Presentation
CS214:presentation Zero-sum Game & von Neumann minimax theorem - - PowerPoint PPT Presentation
CS214:presentation Zero-sum Game & von Neumann minimax theorem Group:Second++ What is a Game Stone Scissors Paper Stone 0,0 +1,-1 -1,+1 Scissors -1,+1 0,0 +1,-1 Paper +1,-1 -1,+1 0,0 What is a Mixed Strategy Stone Scissors
SLIDE 2
SLIDE 3
What is a Mixed Strategy
Stone Scissors Paper Stone 0,0 +1,-1
- 1,+1
Scissors
- 1,+1
0,0 +1,-1 Paper +1,-1
- 1,+1
0,0
1/3 1/3 1/3
SLIDE 4
What is a Pure Strategy
Stone Scissors Paper Stone 0,0 +1,-1
- 1,+1
Scissors
- 1,+1
0,0 +1,-1 Paper +1,-1
- 1,+1
0,0
1
SLIDE 5
What is a Zero-Sum Game
Stone Scissors Paper Stone 0,0 +1,-1
- 1,+1
Scissors
- 1,+1
0,0 +1,-1 Paper +1,-1
- 1,+1
0,0
SLIDE 6
A simpler example
Economy Society Morality Tax-cut
+3,-3
- 1,+1
- 2,+2
+1,-1
Debate in an Election
SLIDE 7
A simpler example
Economy Society Morality Tax-cut
+3
- 1
- 2
+1
1/2 1/2 1/2 1/2 Frog`s profit:
SLIDE 8
Two Scenarios
Frog-Trump:Frog chooses his strategy first Trump-Frog:Trump chooses his strategy first
SLIDE 9
Scenario1:Frog-Trump
Economy Society Morality Tax-cut
+3
- 1
- 2
+1
x1 x2
SLIDE 10
Scenario1:Frog-Trump
Economy Society Morality Tax-cut
+3
- 1
- 2
+1
x1 x2
SLIDE 11
Scenario1:Frog-Trump
(z is the profit of Frog)
SLIDE 12
Scenario2:Trump-Frog
(w is the profit of Frog)
SLIDE 13
Which is bigger?
z or w?
z: Frog-Trump w:Trump-Frog
SLIDE 14
von Neumann`s Theorem
z = w!
z: Frog-Trump w:Trump-Frog
SLIDE 15
Proof
Dual
SLIDE 16