Nash's classical game theory asserts that every player can go down the rabbit hole of "you know that I know that you know that I know" recursion.
This is OK when you have a manageable number of players. Now, if you model 300 million of people voting in election and you don't know the players (say, unconditional hate/skepticism/love of CNN news), then Nash theory becomes prohibitively difficult to compute.
What are the best game theoretical approximations for a large number of players with an ensemble of strategies, varying from perfect to random to perfectly wrong?
First, there are no "wrong" strategies in equilibrium. Nash equilibrium is defined as a profile of strategies which are "right", as in, a best response to all other strategies. So Nash equilibrium already is a simplification of reality: no irrational behavior happens in equilibrium.
Second, in Nash equilibrium, all players know the strategies that all other players use (this knowledge is necessary to play the best response). So it is not the case that players are completely in the dark about what other players are doing. This does not, however, mean that players know which actions other players will take. For example, in a mixed strategy equilibrium, players will know with which probabilities other players take which action, but they do not know the realization of those actions. Still, this consistency requirement, too, is a simplification.
Finally, I would say that academic papers usually simplify the setting itself when they compute Nash equilibria. For example, it is often assumed that players are symmetric (same preferences, same available actions, etc.), or that players use symmetric strategies (meaning all asymmetric equilibria, if they exist, are ignored). Also, the set of possible actions or different preferences (represented by payoffs) is usually very simplified (e.g., only two different actions are possible). And these simplifications usually make the game theoretical models very tractable, but they do result in very simple versions of reality.
Given these simplifications, the number of players is often not an issue. For example, there are game theoretical models with an infinity of players (a continuum) which are very easily solvable.