Is there a ‘change in efficiency theory’?

A standard result in oligopoly models is that the more efficient firms have larger market shares. The main question being answered in this paper is: 'if a firm increases (decreases) its relative efficiency does it increase (decrease) its market share?'. We show that, in two widely used models where more efficient firms have larger equilibrium market shares, it is possible to have a firm getting relatively less (more) efficient than its rivals and, at the same time, increasing (decreasing) its market share.