Advertisement

Decisions in Economics and Finance

, Volume 41, Issue 2, pp 463–487 | Cite as

Advertising a product to face a competitor entry: a differential game approach

  • Alessandra Buratto
  • Stefan WrzaczekEmail author
Article
  • 81 Downloads

Abstract

We analyze a market in which advertising is the dominant marketing tool to create market share. We assume that an incumbent firm dominates the market during an initial stage, and that a new competitor is going to enter the market. In particular, we analyze the different advertising policies that the incumbent firm can adopt, before and after the entry of the rival. We explore three possible behaviours. In the first scenario the firm knows that the competitor will arrive at a given instant. In the second one we assume the original firm to be surprised, in the sense that it does not anticipate the entry of the opponent either because it does not expect the competitor to arrive, or it is not prepared to react before the entry takes place. Finally, in the third scenario, the original firm knows that the competitor will enter at a constant rate. We characterize a differential game model and compare the firms’ behaviours in a strategic perspective.

Keywords

Differential games Nash equilibria Marketing Market entry 

JEL Classification

C72 C73 L13 D21 

Notes

Acknowledgements

This work was supported by the University of Padova and the project “Changing market structures in intertemporal optimization” of the Austrian Science Fund (No. P25275-G11). The authors would like to thank the anonymous referees for their valuable remarks and suggestions.

References

  1. Bagwell, K., Ramey, G.: Advertising and limit pricing. Rand J. Econ. 19(1), 59–71 (1988)CrossRefGoogle Scholar
  2. Beatty, J.F., Samuelson, S.S.: Business Law and the Legal Environment, 7th edn. Cengage Learning, Boston (2016)Google Scholar
  3. Boukas, E.-K., Haurie, A., Michel, P.: An optimal control problem with a random stopping time. J. Optim. Theory Appl. 64(3), 471–480 (1990)CrossRefGoogle Scholar
  4. Dockner, E., Jørgensen, S., V. Long, N., Sorger, G.: Differential Games in Economics and Management Science. Cambridge University Press, Cambridge (2000)CrossRefGoogle Scholar
  5. Eliashberg, J., Jeuland, A.P.: The impact of competitive entry in a developing market upon dynamic pricing strategies. Market. Sci. 5(1), 20–36 (1986)CrossRefGoogle Scholar
  6. Grass, D., Caulkins, J.P., Feichtinger, G., Tragler, G., Behrens, D.A.: Optimal Control of Nonlinear Processes: With Applications in Drugs, Corruption and Terror. Springer, Heidelberg (2008)CrossRefGoogle Scholar
  7. Gromova, E., López-Barrientos, J.D.: A differential game model for the extraction of nonrenewable resources with random initial times: the cooperative and competitive cases. Int. Game Theory Rev. 18(2), 1640004 (2016)CrossRefGoogle Scholar
  8. Jørgensen, S., Zaccour, G.: Differential Games in Marketing. Kluwer Academic, Boston (2004)CrossRefGoogle Scholar
  9. Kamien, M.I., Schwartz, N.L.: Optimal maintenance and sale age for a machine subject to failure. Manag. Sci. 17, B495–B504 (1970)CrossRefGoogle Scholar
  10. Kotler, P., Armstrong, G.: Principles of Marketing, 17th edn. Pearson, New York (2018)Google Scholar
  11. Kort, P.M., Wrzaczek, S.: Optimal firm growth under the threat of entry. Eur. J. Oper. Res. 246(1), 281–292 (2015)CrossRefGoogle Scholar
  12. Morgan, W., Katz, M.L., Rosen, H.S.: Microeconomics. McGraw-Hill Education, New York (2009)Google Scholar
  13. Prasad, A., Sethi, S.P.: Competitive advertising under uncertainty: a stochastic differential game approach. J. Optim. Theory Appl. 123(1), 163–185 (2004)CrossRefGoogle Scholar
  14. Prasad, A., Sethi, S.P., Naik, P.A.: Understanding the impact of churn in dynamic oligopoly markets. Automatica 48(11), 2882–2887 (2012)CrossRefGoogle Scholar
  15. Sethi, S.P.: Optimal control of the Vidale–Wolfe advertising model. Oper. Res. 21, 998–1013 (1973)CrossRefGoogle Scholar
  16. Sethi, S.P.: Deterministic and stochastic optimization of a dynamic advertising model. Optim. Control Appl. Methods 4(2), 179–184 (1983)CrossRefGoogle Scholar
  17. Sorger, G.: Competitive dynamic advertising. A modification of the case game. J. Econ. Dyn. Control 13(1), 55–80 (1989)CrossRefGoogle Scholar
  18. Tsai, C.F., Chen, M.Y.: Variable selection by association rules for customer churn prediction of multimedia on demand. Expert Syst. Appl. 37(3), 2006–2015 (2010)CrossRefGoogle Scholar
  19. Vidale, M.L., Wolfe, H.B.: An operations-research study of sales response to advertising. Oper. Res. 5, 370–381 (1957)CrossRefGoogle Scholar

Copyright information

© Associazione per la Matematica Applicata alle Scienze Economiche e Sociali (AMASES) 2018

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of PadovaPaduaItaly
  2. 2.Wittgenstein Centre (IIASA, VID/ÖAW, WU), VID/ÖAWViennaAustria

Personalised recommendations