# Feb 10, 2011 - 10/02/2011 Unpredictability CH 7 OF Thinking...

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10/02/2011 Unpredictability CH 7 OF Thinking Strategically CH 5 OF The Art of Strategy If the Rival has common knowledge, he can predict your best response. Does not know, he cannot predict your best response In a Zero sum game, the objectives are mutually antagonistic. Pure strategies have clear options. Randomized or mixed strategies are a way of being unpredictable. Matching Pennies Steve Kate Head Tail Head +1*,-1 -1,+1* Tail -1,+1* +1*,-1 There is no pair of strategies with mutual best responses. There are two types of Nash Equilibriums- Pure strategy and mixed strategy. Will it hurt if the opponent knows your strategy if it is a pure strategy mixed equilibrium- Yes Then you randomize your strategies 80:20 Randomize Steve 75%, 25% H, T Kate’s Choice Kate’s Expected Pay o f Weight by Probability- Head (+1c)0.75+ 0.25(-1c)= 0.5c Tail 0.75(-1c)+ (0.25) (+1c) = -.5c

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Mixed Strategy – playing heads for kate is a better option as she will win 75% of the times if Steve plays a pure strategy. Right proportion to mix without any regrets is Kate 50, 50, Steve 50, 50
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Feb 10, 2011 - 10/02/2011 Unpredictability CH 7 OF Thinking...

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