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what I claim is the equilibrium strategy 1/3, 1/3, 1/3
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against 1/3, 1/3, 1/3, I get 0
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and if I played any other strategy I'd still get 0,
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Is that right?
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So therefore playing 1/3, 1/3, 1/3 is indeed a best response,
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albeit weakly, it is indeed a best response
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and this is in fact a Nash Equilibrium.
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So what we've shown here is in "Rock, paper, scissors"
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playing 1/3,1/3,1/3 against
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the other guy playing 1/3,1/3,1/3 is a best response,
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anything would be a best response,
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but in particular it's a best response.