Psychology would suggest that this situation is akin to the prisoner's dilemma except...it's you vs. 1 million other prisoners. The higher the stakes for you OR the greater the distribution of others, the more likely we are to end up with a sub-optimal outcome for all.
Alternatively, it's the Richard Feynman Manhattan project writ large: in that instance Feynman was recruited for the project and told to report to Los Alamos but was warned explicitly NOT to book passage directly lest the Germans were watching all of our top scientists and saw that they ALL were headed to Los Alamos. Feynman, correctly assuming that EVERY other world-class physicist had been given the same explicit direction deduced that he'd be fine booking straight to Los Alamos since no one else would be! Indeed, he humorously deduced that his duty was to book directly to Los Alamos since no one else would be doing it and it'd look weird to the Germans in NO ONE was booking directly to Los Alamos. Anyway, it was an amusing anecdote but instructive that even our best and brightest are capable of disobeying direct instruction in even the most high-stakes circumstances.