CS214:presentation Zero-sum Game & von Neumann minimax theorem - PowerPoint PPT Presentation

Oct 15, 2022 •334 likes •505 views

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

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 Paper Stone 0,0 +1,-1 -1,+1 1/3 Scissors -1,+1 0,0 +1,-1 1/3 Paper +1,-1 -1,+1 0,0 1/3
What is a Pure Strategy Stone Scissors Paper Stone 0,0 +1,-1 -1,+1 1 Scissors -1,+1 0,0 +1,-1 0 Paper +1,-1 -1,+1 0,0 0
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
A simpler example Debate in an Election Morality Tax-cut +3,-3 -1,+1 Economy -2,+2 +1,-1 Society
A simpler example 1/2 1/2 Morality Tax-cut +3 -1 1/2 Economy -2 +1 1/2 Society Frog`s profit:
Two Scenarios Frog-Trump:Frog chooses his strategy first Trump-Frog:Trump chooses his strategy first
Scenario1:Frog-Trump Morality Tax-cut +3 -1 x 1 Economy -2 +1 x 2 Society
Scenario1:Frog-Trump Morality Tax-cut +3 -1 x 1 Economy -2 +1 x 2 Society
Scenario1:Frog-Trump (z is the profit of Frog)
Scenario2:Trump-Frog (w is the profit of Frog)
Which is bigger? z or w? z: Frog-Trump w:Trump-Frog
von Neumann`s Theorem z = w! z: Frog-Trump w:Trump-Frog
Proof Dual
Thank you! Q & A

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