The difference of student’s example and Fermi paradox example is that each student knows his number, but civilizations can’t exchange information, so they don’t know each other order numbers in the game. If all civilizations would think that there were around 100 civilizations before them, they all will try the same strategy, and all will fail. That is why some randomization is needed in Fermi case—just to escape behavior paths of those civilizations, who had completely the same information as you.
But if we could use some external counter, like a time after the beginning of the universe, to choose between different strategies, this could help escape randomisation which is less optimal than the strategy of choosing best alternative after N.
The difference of student’s example and Fermi paradox example is that each student knows his number, but civilizations can’t exchange information, so they don’t know each other order numbers in the game. If all civilizations would think that there were around 100 civilizations before them, they all will try the same strategy, and all will fail. That is why some randomization is needed in Fermi case—just to escape behavior paths of those civilizations, who had completely the same information as you.
But if we could use some external counter, like a time after the beginning of the universe, to choose between different strategies, this could help escape randomisation which is less optimal than the strategy of choosing best alternative after N.