# 167hw4 - Game Theory Steven Heilman Please provide complete...

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Game Theory Steven Heilman Please provide complete and well-written solutions to the following exercises. Due February 9th, in the discussion section. Homework 4 Exercise 1. Find the value of the two-person zero-sum game described by the payoff matrix 0 9 1 1 5 0 6 7 2 4 3 3 Exercise 2. Find the value of the two-person zero-sum game described by the payoff matrix 0 7 0 6 4 4 3 3 8 2 6 0 Exercise 3. This Exercise shows that von Neumann’s Minimax Theorem no longer holds when we consider games for three or more players. first, note that there is a suitable generalization of this theorem to two-player general-sum games. That is if A is the payoff matrix for player I and B is the payoff matrix for player II , then max x Δ m min y Δ n x T Ay = min y Δ n max x Δ m x T Ay. max x Δ m min y Δ n x T By = min y Δ n max x Δ m x T By. In words, the first equality says: the maximum over player I ’s strategies followed by the

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• Fall '08
• staff
• Game Theory, Minimax, payoff matrix, Minimax Theorem, two-person zero-sum game, min max xT

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