We argue that, in a simple setting, the relation between the intensity of competition and cost-reducing investment is U-shaped. We consider a two-stage game with cost-reducing investments followed by a linear differentiated Cournot duopoly. We first show that, except for firms that are much less...

The paper characterizes the mixed-strategy equilibria in all-pay auctions with endogenous prizes that depend positively on own effort and negatively on the effort of competitors. Such auctions arise naturally in the context of investment games, lobbying games, and promotion tournaments. We also...