Moral Hazard, Bertrand Competition, and Natural Monopoly

In the traditional model of Bertrand price competition among symmetric firms, there is no restriction on the number of firms that are active in equilibrium. A symmetric equilibrium exists with the different firms sharing the market. I show that this does not hold if we preserve the symmetry between firms but introduce moral hazard with a customer-sensitive probability of exposure; competition necessarily results in a natural monopoly with only one active firm. Sequential price announcements and early adoption are some equilibrium selection mechanisms that help to pin down the identity of the natural monopolist. If we modify the standard Bertrand assumptions to introduce decreasing returns to scale, a natural oligopoly will emerge instead of a natural monopoly. The insights of the basic model are robust to many extensions.