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In this paper, we extend to a general equilibrium context Bertrand's classic critique of Cournot. We present a game-theoretic model of a pure exchange, monetary economy, in which buyers as well as sellers announce both quantities and prices. When buyers act strategically, the "Edgeworth nonexistence problem" is circumvented: under weak conditions, a pure strategy Nash equilibrium exists for this game. We make precise the Bertrand idea that when agents in a finite economy are permitted to compete-by-price the resulting allocations will be competitive. Specifically, the Nash equilibria for our game yield allocations that are "competitive" allocations for the underlying exchange economy, provided that there are at least two buyers and two sellers actively trading in every market. Under this characterization of strategic behaviour, then, "two is enough for competition."