The argument that there is a strategic advantage to being the first to act. For example, in a Stackelberg duopoly with homogeneous compared to the level obtained when moves are made simultaneouslv. As in compared to the level obtained when moves are made simultaneously, as in Coumot competition. Not all games are characterized by first-mover advantage (consider playing paper-stone-scissors with sequential moves).
Reference: Oxford Press Dictonary of Economics, 5th edt.