Potential solutions of the $n$-player Prisoner's Dilemma Suppose we want to model a real-world phenomenon as an $n$-player Prisoner's Dilemma.

To be more specific, suppose we use RM Dawes' paper "The commons dilemma game: An n-person mixed-motive game with a dominating strategy for defection, 1973" which generally formalize the Prisoner's Dilemma for $n$ players along with a tragedy of the commons (Hardin's tragedy 1968).

Although modelling might seem "easy," how one can properly analyze in Game theory? How can we justify the validity of the game with the real world?

Also, even if we model the real-world phenomenon as a Prisoner's Dilemma, what would be some of the potential solutions to prevent the tragedy?

To be more exact, what are some of the standard methodologies to prevent universal defection?

I'd appreciate any help.
All the insights to your question about the n-player game carry over from the 2-player game. 

The validity in the real world is justified to the extent and in the same way as for the 2-player game, with all its caveats. An n-player game, however is even more realistic, because it is more general and many economic issues involve more than 2 players. Consider for example global geopolitical issues that require coordination, such as climate change or nuclear bombs. 

The potential solutions are the same as for the 2-player game as well. Notably, in repeated games over time, reputational effects and retaliation can matter. If those who play the non-cooperative strategy (which is the "bad" action that leads to the prisoner's dilemma outcome that is worse for everyone) are punished over time, then the problem you describe can be overcome. Denesp in his comment to this answer gives some examples.

The reason a static prisoner's dilemma always has a non-pareto-optimal equilibrium (i.e. why it poses a societal problem) is because it is played once or is a one-shot game without the possibility to punish deviators later on. If players interact frequently with each other, (the threat of) retaliation can help overcome the dilemma. There are a number of such strategies. One of the more famous ones to look up would be "tit for tat".