What process can lead to Nash equilibrium (or a strategy profile close to NE) actually being played in a game, when real humans are the players?
Consider a game, where rationalising is sufficiently difficult, so that some players do not rationalize about their own and their opponent's actions in a sufficient enough dept so as to arrive at the NE solution. Then some other strategy profile will be played.
Now to justify exploring and caring about NE in various systems (eg. oligopoly market), there has to be some process, that makes even boundedly rational players play NE. Maybe it could be learning from interaction, or communication and agreeing on an action profile...
My question is, if there is some study or experiment that would show us, that caring about NE makes sence, because real-life game strategies tend (possibly after some time) towards NE.
Here is an article and a paper linked to therein that appear to deal with your question.