Comparison of Bertrand and Cournot competitions under random yield

We look at a Bertrand model in which each firm may be unreliable with random yield, so the total quantity brought into market is uncertain. Under mild conditions, the Bertrand model with random yield has a unique Nash equilibrium, in which the prices and production quantities are determined by each firm's production cost and reliability. In the case of symmetric firms, we compare Bertrand competition with Cournot competition by numerical examples, and find that Bertrand competition yields lower prices and less profits than Cournot competition. Furthermore, in the case of symmetric firms with 0-1 yields, we explicitly show that Bertrand competition yields lower prices and less profits than Cournot competition, and the comparison between the quantities of Bertrand and Cournot competition is dependent on the value of reliability. When the reliability is high, Cournot competition yields less quantities than Bertrand competition. Otherwise, the other hand holds.