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I understand the reason why mixed strategy Nash equilibrium exists. But what are the conditions for the existence of pure strategy Nash equilibrium?

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The most simple example is the example of unlimited periods and Bertrand pricing, in any given period the "pure strategy" (with 2 firms) is to produce 1/2 of monopolist quantity and sell at monopolist price and recieve profits = π(1-d)^t Where d is discount value t is period Any deviation will result in 0 profits every period following the deviation, thus in an infinite period model is not worth it.

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