Is there a word or phrase that encapsulates this recurrent scenario? Let me give a couple examples.
A limited amount of land is cheap or free in a given area. The people who get there first get all the land. They can then set the price so that people who come later and still want land might end up paying much much more. This applies to any limited resource that is desirable.
On sister site Stackoverflow people ask programming questions. The first people who asked and answered the most basic questions about given languages in the early stages of the site received thousands of upvotes and reputation points. Basic questions are broadly applicable to learners of a programming language, so whoever was there first is by far the most visible and rewarded. Those questions can never be asked again (in theory) without being marked as duplicates.
"Early adopters" comes to mind, but it's limited in scope and only partially applicable as a category of people. The phrase doesn't imply that there are definite, intrinsic, and limited benefits to gain by being among the first to do something, benefits which will not be available, or available in diminishing amounts, to later arrivals because they will have already been used up or claimed.