Is there experimental evidence that people ever play mixed Nash equilibrium in real games?
Have any studies been done that demonstrate people (not game theorists) actually using mixed Nash equilibrium as their strategy in a game?
According to this(article about mixed equilibrium strategies), I think penalty kicks between two soccer teams use mixed Nash equilibrium strategies.
There have been lots of studies on this sort of thing, with different results. It depends a lot on cultural context. You might look at "A Beautiful Math" by Tom Siegfried