I construct an endogenous growth model where R&D is carried out at the industry level in a game of innovation between leaders and followers. Innovation costs for followers are assumed to increase with the technological lag from leaders. We obtain three results that contrast with standard Schumpeterian models, such as Aghion and Howitt (1992). First, leaders may innovate in equilibrium, in an attempt to force followers out of the innovation game. Second, policies (such as patents) that allow for strong protections of monopolies can reduce the steady state growth rate of the economy. Third, multiple equilibria arise when monopolies' protection is large.