How does product market competition influence whether CEOs with greater or lower levels of overconfidence are hired and whether CEOs overinvest in innovation? In a Cournot model in which firms hire a CEO to take charge of research and development (R&D) investment and production decisions, this paper shows that CEO overconfidence and overinvestment can be explained as an equilibrium outcome. More importantly, the intensity of product market competition and the equilibrium CEO overconfidence level (and R&D investment) exhibit an inverted U-shaped relationship. As the product market tends toward perfect competition, all firms hire a realistic CEO and do not overinvest. Copyright © 2014 John Wiley & Sons, Ltd.