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if everyone else is randomizing,
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the towns will in fact be, at least asymptotically,
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the towns will be equally mixed
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and you'll be happy to randomize.
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Why? Because you'll be indifferent
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whether you end up in East Town or West Town,
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so you may as well toss a coin anyway.
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So this is actually another Nash Equilibirum.
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I'm being a bit loose here but we'll be much more precise in a moment.
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There's another Nash Equilibrium in this model,
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and it isn't as silly in some sense as
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having everyone going to East Town