Advertisement

Supply Chain Network Oligopolies with Product Differentiation

  • Anna Nagurney
  • Dong Li
Chapter
Part of the Springer Series in Supply Chain Management book series (SSSCM, volume 2)

Abstract

This chapter is the first chapter of Part III of this book, which concentrates on quality in product differentiation and outsourcing settings. In Chap. 3, we noted that quality information asymmetry under product homogeneity could lead to a quality “free ride,” which might jeopardize certain firms’ profits and product quality. Therefore, in order to prevent such harmful results, it is important for firms to differentiate their products from that of their competitors, so that consumers will be able to identify the products of different firms and their quality. In this chapter, we present a supply chain network model with quality competition in differentiated products, where the product of each firm is substitutable but differentiated by a brand or label. We first present the equilibrium model and derive alternative variational inequality formulations. We then construct the projected dynamical systems model, which provides a continuous-time evolution of the firms’ product shipments and product quality levels. The stability analysis results are also presented, and a discrete-time version of the continuous-time adjustment process is constructed, which yields an algorithm with closed form expressions at each iteration. The algorithm is then utilized to compute solutions to several numerical examples. We also include sensitivity analysis results for minimum quality standards. The framework developed in this chapter can serve as the foundation for the modeling and analysis of competition among firms in industries ranging from food to pharmaceuticals to durable goods and high tech products, as well as Internet services, where quality and product differentiation are seminal.

Keywords

Variational Inequality Product Differentiation Quality Level Supply Chain Network Product Shipment 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

References

  1. Acharyya, R. (2005). Consumer targeting under quality competition in a liberalized vertically differentiated market. Journal of Economic Development, 30(1), 129–150.Google Scholar
  2. Anderson, S. P., & Palma, A. (2001). Product diversity in asymmetric oligopoly: Is the quality of consumer goods too low? The Journal of Industrial Economics, 49(2), 113–135.CrossRefGoogle Scholar
  3. Aoki, R. (1991). R&D competition for product innovation: An endless race. American Economic Review, 81(2), 252–256.Google Scholar
  4. Berndt, E. R., Bui, L., Reily, D. R., & Urban, G. L. (1995). Information, marketing, and pricing in the U.S. antiulcer drug market. The American Economic Review, 85(2), 100–105.Google Scholar
  5. Bernstein, J., & Nadiri, M. I. (1991). Product demand, cost of production, spillovers, and the social rate of return to R&D (NBER Working Paper No. 3625). Cambridge.Google Scholar
  6. Bischi, G. I., Chiarella, C., Kopel, M., & Szidarovsky, F. (2009). Nonlinear oligopolies: Stability and bifurcations. Berlin: Springer.Google Scholar
  7. Cohen, W. M., & Klepper, S. (1996). Firm size and the nature of innovation within industries: The case of process and product R&D. The Review of Economics and Statistics, 78(2), 232–243.CrossRefGoogle Scholar
  8. Cournot, A. A. (1838). Researches into the mathematical principles of the theory of wealth (English Trans.). London: MacMillan.Google Scholar
  9. Dafermos, S., & Nagurney, A. (1987). Oligopolistic and competitive behavior of spatially separated markets. Regional Science and Urban Economics, 17, 245–254.CrossRefGoogle Scholar
  10. D’Aspremont, C., Gabszewicz, J. J., & Thisse, J. F. (1979). On Hotelling’s “Stability in competition”. Econometrica, 47, 1145–1150.CrossRefGoogle Scholar
  11. Dixit, A. K., & Stiglitz, J. E. (1977). Monopolistic competition and optimum product diversity. American Economic Review, 67(3), 297–308.Google Scholar
  12. Dupuis, P., & Nagurney, A. (1993). Dynamical systems and variational inequalities. Annals of Operations Research, 44, 9–42.CrossRefGoogle Scholar
  13. Economides, N. (1989). Quality variations and maximal differentiation. Regional Science and Urban Economics, 19, 21–29.CrossRefGoogle Scholar
  14. Gabay, D., & Moulin, H. (1980). On the uniqueness and stability of Nash equilibria in noncooperative games. In A. Bensoussan, P. Kleindorfer, & C. S. Tapiero (Eds.), Applied stochastic control in econometrics and management science (pp. 271–294). Amsterdam: North-Holland.Google Scholar
  15. Holcombe, R. G. (2009). Product differentiation and economic progress. The Quarterly Journal of Austrian Economics, 12(1), 17–35.Google Scholar
  16. Hotelling, H. (1929). Stability in competition. The Economic Journal, 39(153), 41–57.CrossRefGoogle Scholar
  17. Johnson, J. P., & Myatt, D. P. (2003). Multiproduct quality competition: Fighting brands and product line pruning. American Economic Review, 93(3), 748–774.CrossRefGoogle Scholar
  18. Lilien, G. L., & Yoon, E. (1990). The timing of competitive market entry: An exploratory study of new industrial products. Management Science, 36(5), 568–585.CrossRefGoogle Scholar
  19. Masoumi, A. H., Yu, M., & Nagurney, A. (2012). A supply chain generalized network oligopoly model for pharmaceuticals under brand differentiation and perishability. Transportation Research E, 48, 762–780.CrossRefGoogle Scholar
  20. Matsumoto, A., & Szidarovsky, F. (2011). Price and quantity competition in dynamic oligopolies with product differentiation. Revista Investigacion Operacional, 32(3), 204–219.Google Scholar
  21. Motta, M. (1993). Endogenous quality choice: Price vs. quantity competition. The Journal of Industrial Economics, 41(2), 113–131.CrossRefGoogle Scholar
  22. Nagurney, A. (1999). Network economics: A variational inequality approach (2nd and Rev. ed.). Boston: Kluwer Academic.CrossRefGoogle Scholar
  23. Nagurney, A., Dupuis, P., & Zhang, D. (1994). A dynamical systems approach for network oligopolies and variational inequalities. Annals of Regional Science, 28, 263–283.CrossRefGoogle Scholar
  24. Nagurney, A., & Li, D. (2014). A dynamic network oligopoly model with transportation costs, product differentiation, and quality competition. Computational Economics, 44(2), 201–229.CrossRefGoogle Scholar
  25. Nagurney, A., Yu, M., Masoumi, A. H., & Nagurney, L. S. (2013). Networks against time: Supply chain analytics for perishable products. New York: Springer.CrossRefGoogle Scholar
  26. Nagurney, A., & Zhang, D. (1996). Projected dynamical systems and variational inequalities with applications. Boston: Kluwer Academic.CrossRefGoogle Scholar
  27. Nash, J. F. (1950). Equilibrium points in n-person games. Proceedings of the National Academy of Sciences, USA, 36, 48–49.Google Scholar
  28. Nash, J. F. (1951). Noncooperative games. Annals of Mathematics, 54, 286–298.CrossRefGoogle Scholar
  29. Schumpeter, J. A. (1943). Capitalism, socialism and democracy (3rd ed.). London: George Allen and Unwin.Google Scholar
  30. Shankar, V., Carpenter G. S., & Krishnamurthi, L. (1998). Late mover advantage: How innovative late entrants outsell pioneers. Journal of Marketing Research, 35(1), 54–70.CrossRefGoogle Scholar
  31. Steiner, M., Bugen, D., Kazanchy, B., Knox, W., Prentice, M. V., & Goldfarb, L. S. (2007). The continuing evolution of the pharmaceutical industry: Career challenges and opportunities. Chatham: Regent Atlantic Capital, white paper.Google Scholar
  32. Yu, M., & Nagurney, A. (2013). Competitive food supply chain networks with application to fresh produce. European Journal of Operational Research, 224(2), 273–282.CrossRefGoogle Scholar
  33. Zhang, D., & Nagurney, A. (1995). On the stability of projected dynamical systems. Journal of Optimization Theory and Its Applications, 85, 97–124.CrossRefGoogle Scholar

Copyright information

© Springer International Publishing Switzerland 2016

Authors and Affiliations

  • Anna Nagurney
    • 1
  • Dong Li
    • 2
  1. 1.Isenberg School of ManagementUniversity of MassachusettsAmherstUSA
  2. 2.Department of Management and Marketing College of BusinessArkansas State UniversityState UniversityUSA

Personalised recommendations