<p>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.</p>

CC BY-SA 3.0
2017-04-25T13:44:28.010Z
2017-04-25T13:44:28.010Z
Nik
<p>I understand the reason why mixed strategy Nash equilibrium exists. But what are the conditions for the existence of pure strategy Nash equilibrium?</p>

<game-theory><nash-equilibrium>
Existence of pure strategy Nash equilibrium
Tony
# Existence of pure strategy Nash equilibrium

(Asked by: username_0 on 2017-04-25)

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

**Tags:** game-theory, nash-equilibrium

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## 1 answers

### Answer by username_1 on 2017-04-25. Score: -2

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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