The duopoly model with a Cournot form under random yield has received little attention. This article revisits the classic Cournot duopoly competition model by considering manufacturer yield uncertainty. We analyze the model under symmetric, asymmetric and monopoly situations. The manufacturers’ best production policy and expected market share are compared with each other in each situation. The expected market outputs of the three models are also compared under certain conditions. In the asymmetric case, the asymmetric model is extended by considering a powerful oligarch who can exert influence on her rival’s production decision by releasing her cost-type information. We derive that the maximization of the stronger manufacturer’s expected profit is highly correlated with consumer surplus. Numerical examples are presented to illustrate the results.