Bertrand under Uncertainty: Private and Common Costs*

Abstract

Does asymmetric information about costs in a homogeneous-good Bertrand model soften competition? Earlier literature has shown that the answer (perhaps counter-intuitively) is “no,” while assuming (i) private (i.e., independent) cost draws and (ii) no drastic innovations. I first show, in a fairly general setting, that by relaxing (i) and instead allowing for sufficiently much common (interdependent) cost draws, asymmetric information indeed softens competition. I then study a specification that yields a closed-form solution and show that relaxing (ii) but not (i) does not alter the result in the earlier literature. While relying on specific functional forms, this specification is quite rich and might be useful in applications. It allows for any (positive) degree of interdependence between the cost draws, for any demand elasticity, and for any number of firms. The closed-form solution is simple and in pure strategies.