This paper studies conditions for competitiveness of strategic market games where agents set prices and quantities (a game is said to be competitive if its Nash equilibria are Walrasian). Some necessary conditions are first derived which show that discontinuities in the strategic outcome functions may be an essential element for competitiveness. Then a set of economically meaningful sufficient conditions for competitiveness are derived. These bridge the gap between visions of competition "a la Bertrand" and some recent non-Walrasian concepts.