Existence of pure strategy Nash equilibrium
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.