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Game theory: Nash, minimax, LP
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Module 2
Zero-Sum Games and the Minimax Theorem
1
Two-Player Zero-Sum Games: Maximin and Minimax
Define two-player zero-sum games and the associated maximin and minimax values.
2
Maximin ≤ Minimax: The Easy Direction
Prove that the maximin value is always less than or equal to the minimax value (the 'easy' direction of the theorem).
3
Minimax Theorem and Nash Equilibrium
State von Neumann's minimax theorem and relate the value of the game to Nash Equilibrium.
Nash Equilibrium and Minimax in Zero-Sum Games
Prove that a strategy profile is a Nash equilibrium in a zero-sum game if and only if it is a minimax solution.
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Game Theory Fundamentals and Nash Equilibrium
Next module
Linear Programming and Duality Theory