La grenouille qui se peut faire aussi grosse que le boeuf

Quite often, a firm has to decide between investing in a safe project (``small'') where rewards and losses remain moderate and a risky alternative (``big'') where the rewards and the losses are larger. We study such a choice in a context where the probability of success depends both on the intrinsic ability of the firm and on the choice of an other firm which is a follower. The ability of the follower is unknown to the leader and vice-versa. We show that a leader with a poor ability selects the big project as well as a leader with a very high ability. On the other hand a leader with a medium ability prefers the small project. When weak the follower chooses the small project, when of medium ability it chooses randomly and when of high ability it selects the big project. Information asymmetry, though, prevents the selection of the best firm: a leader with a lower ability can deter competition form a medium or weak follower by selecting the big project.