Limit pricing and secret barriers to entry

We study a two periods entry game where the incumbent firm, who has private information about his own production costs, makes a non observable long run investment choice, along with a pricing decision observed by the entrant. The investment choice affects both post-entry competition and first period cost of production, so that the cost of signaling becomes endogenous. The game is solved following Bayes-Nash requirements, the intuitive criterion is used to constrain off-equilibrium beliefs. When investment is publicly observable, it is shown that the unique intuitive equilibrium is the separating equilibrium with limit pricing and no entry deterrence. When investment is not observable, quite remarkably, there exists a unique intuitive pooling equilibrium which is Pareto superior, from the incumbent's point of view, to the unique intuitive separating equilibrium. In the pooling equilibrium no entry takes place and the price is below the low cost monopoly price. Thus, when investment is secret, a limit pricing policy supports entry deterrence. Our model provides an example of secret barriers to entry and their relationship with limit pricing. We also contribute to the analysis of a relatively under-researched class of games where the cost of signaling unobservable characteristics is endogenously determined by unobserved actions.