I have a very basic question : How is nash equilibrium found in real life problem.
I mean, in theory it exists and we can prove it but how this knowledge will be applied in real life especially with the best response dynamics.
Are the players supposed to know the whole possible strategies of all other players and they will be trying all possible combinations? Or will this equilibrium be found by a central node and the result given to the players?
In a theoretical context, if all players have perfect information and common knowledge of each others' choices, a Nash Equilibrium can occur in any strategic situation between $N$ players. This can occur often in an experimental setting, as shown by some decision scientists.
However, in most realistic situations, most agents do not have perfect information of each others' outcomes, nor does the common knowledge assumption hold. Thus, for most realistic theories related to firm competition and strategic behavior, we assume that each player does not have perfect information about the other agents' outcomes: thus, in a simultaneous and dynamic games with imperfect information, we have Bayesian and Perfect Bayesian Equilibria respectively to represent our "stable points" (see https://en.wikipedia.org/wiki/Bayesian_game to get an overview of these types of games).
An even more relaxed assumption is when each agent does not even have perfect information on each others' strategy sets: this is an example of when someone in a game may have a "secret weapon" that you haven't seen yet. These kinds of issues related to learning a given agent's strategy set is discussed in the literature on learning in games.