A cookie gets implanted by the first aff link clicked.
Some of these are just plain over writeable, so the last aff gets the sale.
Some are for a set period of time, and if the sale comes through another aff during the specified time, the sale goes to the first aff.
All of this is foiled these days by people running anti spyware programs, most of which make it their business to remove cookies without asking.
Some surfers also remove cookies daily for whatever reasons.