A Demonstration of an Application of the Bertrand Network: Guessing the Distribution of Buyers Within the Market

  • Murillo Henrique Pedroso Ferreira
  • João Paulo PereiraEmail author
Conference paper
Part of the Lecture Notes in Information Systems and Organisation book series (LNISO, volume 31)


Bertrand and the Cournot model are one of the most used model for modeling competition between companies. This paper presents a work-in-progress that studies the application of the recently developed Bertrand Network model by using it in a reverse manner: first it is considered that firms are competing in equilibrium, then, after analyzing how companies are choosing prices, it is calculated which distribution of buyers would lead to that equilibrium. An unreal example is presented to help to understand the model. Furthermore, a formula is suggested to expand the networked model to allow a mix of duopolies and oligopolies.


Nash equilibrium Bertrand network Market competition Expanded Bertrand network Market expansion 


  1. Abolhassani, M., Bateni, M. H., Hajiaghayi, M., Mahini, H., & Sawant, A. (2014). Network cournot competition. Lecture Notes in Computer Science (pp. 15–29).Google Scholar
  2. Babaioff, M., Blumrosen, L., & Nisan, N. (2016). Networks of complements. In The 43rd International Colloquium on Automata, Languages and Programming (ICALP). Retrieved from
  3. Babaioff, M., Lucier, B., & Nisan, N. (2013, June). Bertrand networks. In Proceedings of the Fourteenth ACM Conference on Electronic Commerce.
  4. Babaioff, M., Nisan, N., & Paes Leme, R. (2014). Price competition in online combinatorial markets. In Proceedings of the 23rd International Conference on World Wide Web (pp. 711–722). Seoul, Korea: ACM.
  5. Barquin, J., & Vazquez, M. (May, 2008). Cournot equilibrium calculation in power networks: An optimization approach with price response computation. IEEE Transactions on Power Systems, 23(2), 317–326. Scholar
  6. Bimpikis, K., Ehsani, S., & Ilkiliç, R. (2014). Cournot competition in networked markets. In Proceedings of the Fifteenth ACM Conference on Economics and Computation (pp. 733–733). Palo Alto, California, USA: ACM.
  7. Bose, S., Cai, D. W., Low, S. H., & Wierman, A. (2014a). The role of a market maker in networked cournot competition. In arXiv: Computer science and game theory (pp. 4479–4484). Retrieved October 5, 2018, from
  8. Bose, S., Cai, D. W., Low, S., & Wierman, A. (2014b). The role of a market maker in networked cournot competition. In 53rd IEEE Conference on Decision and Control (pp. 4479–4484).
  9. Cai, D., Bose, S., & Wierman, A. (2017). On the role of a market maker in networked cournot competition. Obtido de
  10. Guzmán, C. L. (2011). Price competition on network. Banco de México.Google Scholar
  11. Jing-Yuan, W., & Smeers, Y. (1999). Spatial oligopolistic electricity models with cournot generators and regulated transmission prices. Operations Research, 47(1), 102–112. Scholar
  12. Kasbekar, G. S., & Sarkar, S. (January, 2012). Spectrum pricing games with spatial reuse in cognitive radio networks. IEEE Journal on Selected Areas in Communications, 30(1), 153–164. Scholar
  13. Kreps, D. M., & Scheinkman, J. A. (1983). Quantity Precommitment and bertrand competition yield Cournot outcomes. The Bell Journal of Economics, 14, 326–337. Scholar
  14. Motalleb, M., Eshraghi, A., Reihani, E., Sangrody, H., & Ghorbani, R. (2017). A game-theoretic demand response market with networked competition model. n 2017 North American Power Symposium (NAPS) (pp. 1–6). Morgantown, WV, USA: IEEE.
  15. Yao, J., Oren, S. S., & Adler, I. (2004). Computing Cournot equilibria in two settlement electricity markets with transmission constraint. In 37th Annual Hawaii International Conference on System Sciences.

Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Polytechnic Institute of BragançaBragançaPortugal
  2. 2.UNIAG (Applied Management Research Unit)BragançaPortugal

Personalised recommendations