Is there a U-shaped relation between competition and investment?

We consider a two-stage game with cost-reducing investments followed by a linear differentiated Cournot duopoly. With competition inversely parameterized by the extent of product differentiation, investment in the subgame perfect equilibrium is typically minimal for intermediate levels of competition. Laboratory experiments partly confirm the U-shape in a reduced one-stage version of the game. In the two-stage version, there is no evidence for positive effects of moving from intermediate to intense competition.