Comparison of Bertrand and Cournot competitions under random yield

Abstract

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.

Keywords:

• Bertrand competition
• Cournot competition
• random yield
• oligopoly

Acknowledgements

The authors would like to give their indebted thanks to editor-in-chief Alexandre Dolgui, the associate editor, four anonymous referees for their valuable comments, which help us improve the paper greatly. The first author also thanks the support of Dongguan University of Technology.

Notes

No potential conflict of interest was reported by the authors.

Additional information

Funding

This work was partially supported by National Natural Science Foundation of China [grant number 71201027], [grant number 71571170], [grant number 71272085], [grant number 71401067]; Humanity and Social Science Youth Foundation of Ministry of Education of China [grant number 12YJC630260]; Guangdong Natural Science Foundation [grant number 2014A030313627] and Foundation for Characteristic Innovation in Higher Education of Guangdong.