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Feedback Nash Equilibrium for Dynamic Brand and Channel Advertising in Dual Channel Supply Chain

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Abstract

This paper investigates dynamic brand and channel advertising and their effects on market expansion and market share in a dual channel supply chain by using differential game theory. Nash equilibrium of the differential game will be obtained by the feedback approach. A sensitivity analysis was performed to assess the impact of key parameters on optimal strategies and to characterize behaviors of both the manufacturer and retailer over time. Comparative statistics show that a higher compatibility of a product with online marketing leads to a higher advertising effort for the online channel by the manufacturer, an enhanced steady state for demand of the brand as well as greater sales in the steady state through the online channel.

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References

  1. Cassar, K., Swerdlow, F.S., Kim, H., Johnson, M.: Local commerce: Internet threat mandates brick-and-mortar reconstruction. In: Jupiter Vision Report, vol. 11 (2000)

    Google Scholar 

  2. Brynjolfsson, E., Smith, M.D.: Frictionless commerce? A comparison of Internet and conventional retailers. Manag. Sci. 46(4), 563–585 (2000)

    Article  Google Scholar 

  3. Smith, M.D., Bailey, J., Brynjolfsson, E.: Understanding digital markets: review and assessment. In: Brynjolfsson, E., Kahin, B. (eds.) Understanding Digital Economy. MIT Press, Cambridge (2000)

    Google Scholar 

  4. Chiang, W.Y., Chhajed, D., Hess, J.D.: Direct marketing, indirect profits: a strategic analysis of dual channel supply chain design. Manag. Sci. 49(1), 1–20 (2003)

    MATH  Google Scholar 

  5. Jørsengen, S., Zaccour, G.: Differential Games in Marketing. Kluwer Academic, Boston (2004)

    Book  Google Scholar 

  6. He, X., Prasad, A., Sethi, S.P., Gutierrez, G.J.: A survey of Stackelberg differential game models in supply and marketing channels. J. Syst. Sci. Syst. Eng. 16(4), 385–413 (2007)

    Article  Google Scholar 

  7. Amrouche, N., Martin-Herran, G., Zaccour, G.: Pricing and advertising of private and national brands in a dynamic marketing channel. J. Optim. Theory Appl. 137, 465–483 (2008)

    Article  MATH  MathSciNet  Google Scholar 

  8. Amrouche, N., Martin-Herran, G., Zaccour, G.: Feedback Stackelberg equilibrium strategies when the private label competes with the national brand. Ann. Oper. Res. 164, 79–95 (2008)

    Article  MATH  MathSciNet  Google Scholar 

  9. Karray, S., Zaccour, G.: A differential game of advertising for national and store brands. In: Haurie, A., Zaccour, G. (eds.) Dynamic Games: Theory and Applicatoins, pp. 213–230. Springer, New York (2005)

    Chapter  Google Scholar 

  10. Karray, S., Martin-Herran, G.: A dynamic model for advertising and pricing competition between national and store brands. Eur. J. Oper. Res. 193, 451–467 (2009)

    Article  MATH  MathSciNet  Google Scholar 

  11. Viscolani, B., Zaccour, G.: Advertising strategies in a differential game with negative competitor’s interference. J. Optim. Theory Appl. 140, 153–170 (2009)

    Article  MATH  MathSciNet  Google Scholar 

  12. Jørgensen, S., Taboubi, S., Zaccour, G.: Cooperative advertising in a marketing channel. J. Optim. Theory Appl. 110(1), 145–158 (2001)

    Article  MathSciNet  Google Scholar 

  13. Buratto, A., Grosset, L., Viscolani, B.: Advertising coordination games of a manufacturer and a retailer while introducing a new product. Top 15, 307–321 (2007)

    Article  MATH  MathSciNet  Google Scholar 

  14. He, X., Krishnamoorthy, A., Prasad, A., Sethi, S.P.: Retail competition and cooperative advertising. Oper. Res. Lett. 39, 11–16 (2011)

    Article  MATH  MathSciNet  Google Scholar 

  15. Prasad, A., Sethi, S.P.: Competitive advertising under uncertainty: a stochastic differential game approach. J. Optim. Theory Appl. 123(1), 163–185 (2004)

    Article  MATH  MathSciNet  Google Scholar 

  16. He, X., Prasad, A., Sethi, S.P.: Cooperative advertising and pricing in a stochastic supply chain: feedback Stackelberg strategies. Prod. Oper. Manag. 18(1), 78–94 (2009)

    Google Scholar 

  17. Krishnamoorthy, A., Prasad, A., Sethi, S.P.: Optimal pricing and advertising in a durable-good duopoly. Eur. J. Oper. Res. 200, 486–497 (2010)

    Article  MATH  Google Scholar 

  18. Bass, F.M., Krishnamoorthy, A., Prasad, A., Sethi, S.P.: Generic and brand advertising strategies in a dynamic duopoly. Mark. Sci. 24(4), 556–568 (2005)

    Article  Google Scholar 

  19. Nair, A., Narasimhan, R.: Dynamics of competing with quality- and advertising-based goodwill. Eur. J. Oper. Res. 175, 462–474 (2006)

    Article  MATH  Google Scholar 

  20. Giovanni, P.D.: Quality improvement vs. advertising support: which strategy works better for a manufacturer? Eur. J. Oper. Res. 208, 119–130 (2011)

    Article  MATH  Google Scholar 

  21. Erickson, G.M.: An oligopoly model of dynamic advertising competition. Eur. J. Oper. Res. 197, 374–388 (2009)

    Article  MATH  MathSciNet  Google Scholar 

  22. Grosset, L., Roberti, P., Viscolani, B.: A goodwill model with predatory advertising. Oper. Res. Lett. 39, 419–422 (2011)

    Article  MATH  MathSciNet  Google Scholar 

  23. Huang, J., Leng, M., Liang, L.: Recent developments in dynamic advertising research. Eur. J. Oper. Res. 220, 591–609 (2012)

    Article  MATH  MathSciNet  Google Scholar 

  24. Vidale, M.L., Wolfe, H.B.: An operations research study of sales response to advertising. Oper. Res. 5, 370–381 (1957)

    Article  MathSciNet  Google Scholar 

  25. Nerlove, M., Arrow, K.J.: Optimal advertising policy under dynamic conditions. Economica 39, 129–142 (1962)

    Article  Google Scholar 

  26. Sorger, G.: Competitive dynamic advertising: a modification of the case game. J. Econ. Dyn. Control 13, 55–80 (1989)

    Article  MATH  MathSciNet  Google Scholar 

  27. Liang, T., Huang, J.: An empirical study on consumer acceptance of products in electronic markets: a transaction cost model. Decis. Support Syst. 24, 29–43 (1998)

    Article  Google Scholar 

  28. Yan, R., Guo, P., Wang, J., Amrouche, N.: Product distribution and coordination strategies in a multi-channel context. J. Retail. Consum. Serv. 18, 19–26 (2011)

    Article  Google Scholar 

  29. Hess, J., Gerstner, E., Chu, W.: Controlling product returns in direct marketing. Mark. Lett. 7(4), 307–317 (1996)

    Article  Google Scholar 

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Authors and Affiliations

  1. Department of Industrial Engineering, Iran University of Science & Technology, Tehran, Iran

    Mohammad Kazem Sayadi & Ahmad Makui

Authors
  1. Mohammad Kazem Sayadi
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  2. Ahmad Makui
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Correspondence to Mohammad Kazem Sayadi.

Additional information

Communicated by David G. Hull.

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Sayadi, M.K., Makui, A. Feedback Nash Equilibrium for Dynamic Brand and Channel Advertising in Dual Channel Supply Chain. J Optim Theory Appl 161, 1012–1021 (2014). https://doi.org/10.1007/s10957-013-0479-1

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  • DOI: https://doi.org/10.1007/s10957-013-0479-1

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