Bertrand under Uncertainty: Private and Common Costs

This paper proposes an n-firm homogeneous-good Bertrand model with private information about costs. The model allows for any non-negative correlation between the cost draws and for any demand elasticity but still yields a closed-form solution. The solution is simple, in pure strategies, and involves price dispersion. For some parameter values, a weak version of the winner’s curse arises. This framework is used to study the question whether cost uncertainty softens competition. Earlier literature has shown that the answer (perhaps counter-intuitively) is “no,” while assuming (i) independent cost draws and (ii) no drastic innovations. The analysis here shows that relaxing (ii) but not (i) does not alter that result. However, when the cost draws are sufficiently highly correlated and the price elasticity of demand is sufficiently low, cost uncertainty indeed softens competition.