In economics, a zero sum game is:

a mathematical representation of a situation in which a participant’s gain (or loss) of utility is exactly balanced by the losses (or gains) of the utility of the other participant(s). If the total gains of the participants are added up, and the total losses are subtracted, they will sum to zero. Thus cutting a cake, where taking a larger piece reduces the amount of cake available for others, is a zero-sum game if all participants value each unit of cake equally (see marginal utility). In contrast, non–zero sum describes a situation in which the interacting parties’ aggregate gains and losses are either less than or more than zero. A zero-sum game is also called a strictly competitive game while non–zero-sum games can be either competitive or non-competitive. Zero-sum games are most often solved with the minimax theorem which is closely related to linear programming duality,[1] or with Nash equilibrium.

http://en.wikipedia.org/wiki/Zero-sum_game

It really is fiat vs Bitcoin. After all, it is billions of dollar equivalents all around the world that are being converted into Bitcoin. There is nothing that Bitcoin can gain but at the expense of some fiat currency somewhere because the fiat “bad money” (see Gresham’s Law) has chased “good money (i.e. Bitcoin) out of circulation. So the obvious is that fiat money is coming out of savings into fiat currency and being replaced as the money of choice for savings.

So there really is a zero-sum game going on between Bitcoin and fiat and as Bitcoin grows it comes at the expense of fiat. But fiat can create all it wants out of thin air so should fiat worry? Well, yes, of course because the Bitcoin gains are, indeed gains. If the fiat just “papers over” their losses and doesn’t write them down they will weaken their currencies even further than they already are. Weakening currency will simply fuel the flight of an even greater flight of fiat to Bitcoin speeding fiat’s demies.