Investigating the role of customer churn in the optimal allocation of offensive and defensive advertising: the case of the competitive growing market

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The paper investigates the optimal allocation between defensive and offensive advertising efforts in a dynamic, growing market in which two companies are competing for market share. The study described in this paper extends the existing literature on dynamic advertising competition by considering a market that is in the growth phase and by including the heterogeneous decay rate of market share. A modified Lanchester is employed to describe the dynamics of market share by model. The goal of companies operating in this domain is to maximize their profits over a finite decision horizon. Based on the differential game approach the Markovian Nash strategies for offensive and defensive advertising activities are determined. Additionally, an analysis of the extent to which this solution is sensitive to changes in potential market and the rate of customer churn is made.

Agarwal, R., & Bayus, B. L. (2002). The market evolution and take-off of product innovations. SSRN Electronic Journal, 48(8), 1024-1041.

Ahn, J. H., Han, S. P., & Lee, Y. S. (2006). Customer churn analysis: churn determinants and mediation effects of partial defection in the Korean mobile telecommunications service industry. Telecommunications Policy, 30(10-11), 552-568.

Amrouche, N., Martin-Herran, G., & Zaccour, G. (2008). Pricing and advertising of private and national brands in a dynamic marketing channel. Journal of Optimization Theory and Applications, 137(3), 465-483.

Bagwell, K. (2007). The economic analysis of advertising. Handbook of Industrial Organization, 3, 1701-1844.

Bass, F. M., Krishnamoorthy, A., Prasad, A., & Sethi, S. P. (2005a). Advertising competition with market expansion for finite horizon firms. Journal of Industrial and Management Optimization, 1(1), 1-19.

Chandy, R. K., Tellis, G. J., MacInnis, D. J., & Thaivanich, P. (2001). What to say when: advertising appeals in evolving markets. Journal of Marketing Research, 38(4), 399-414.

Chintagunta, P. K., & Vilcassim, N. J. (1992). An empirical investigation of advertising strategies in a dynamic duopoly. Management Science, 38(9), 1230-1244.

Crettez, B., Hayek, N., & Zaccour, G.. (2018). Existence and uniqueness of optimal dynamic pricing and advertising controls without concavity. Operations Research Letters, 46(2), 199-204.

Davidson, H., & Keegan, W. J. (2004). Offensive marketing, Elsevier, Amsterdam.

Deal, K. R. (1979). Optimizing advertising expenditures in a dynamic duopoly. Operations Research, 27(4), 682-692.

Dekimpe, M. G., & Hanssens, D. M. (1995). The persistence of marketing effects on sales. Marketing Science, 14(1), 1-21.

Dragone, D., Lambertini, L. & Palestini, A. (2010). The Leitmann-Schmitendorf advertising game with n players and time discounting. Applied Mathematics and Computation, 217(3), 1010-1016.

Erickson, G. M. (1985). A model of advertising competition. Journal of Advertising Research, 22(3), 297-304.

Erickson, G. M. (1992). Empirical analysis of closed-loop duopoly advertising strategies. Management Science, 38(12), 1732-1749.

Erickson, G. M. (1993). Offensive and defensive advertising: closed-loop duopoly strategies. Advertising Letters, 4(4), 285-295.

Erickson, G. M. (1995). Advertising strategies in a dynamic oligopoly. Journal of Marketing Research, 32(2), 233-237.

Erickson, G. M. (2009). An oligopoly model of dynamic advertising competition. European Journal of Operational Research, 197(1), 374-388.

Feichtinger, G. (1983). The Nash solution of an advertising differential game: generalization of a model by Leitmann and Schmitendorf. IEEE Transactions on Automatic Control, 28(11), 1044-1048.

Fruchter, G. E. (1999). Short communications-oligopoly advertising strategies with market expansion. Optimal Control Applications and Methods, 20(4), 199-212.

Fruchter, G. E., & Kalish, S. (1997). Closed-loop advertising strategies in a duopoly. Management Science, 43(1), 54-63.

Grosset, L., & Viscolani, B. (2015). Open-loop Nash equilibrium in Erickson’ s oligopoly model. Nonlinear Analysis and Differential Equations, 3(4), 167-172.

Hamilton, R. W., Rust, R. T., & Dev, C. S. (2017). Which features increase customer retention?. MIT Sloan Management Review, 58(2), 79-84.

Hogan, J. E., Lemon, K. N., & Libai, B. (2003). What is the true value of a lost customer?. Journal of Service Research, 5(3), 196-208.

Jarrar, R., Martin-Herran, G., & Zaccour, G. (2004). Markov perfect equilibrium advertising strategies of Lanchester duopoly model: a technical note. Management Science, 50(7), 995-1000.

Jorgensen, S., & Sigue, S.-P. (2015). Defensive, offensive, and generic advertising in a Lanchester model with market growth. Dynamic Games and Applications, 5(4), 523-539.

Jorgensen, S., & Zaccour, G. (2012). Differential games in advertising. New York: Springer Science & Business Media.

Kamien, M. I., & Schwartz, N. L. (2012). Dynamic optimization: the calculus of variations and optimal control in economics and management. New York: Dover Publications, Inc.

KhakAbi, S., Gholamian, M. R., & Namvar, M.. (2010). Data mining applications in customer churn management. ISMS 2010 - UKSim/AMSS 1st International Conference on Intelligent Systems, Modelling and Simulation, 220-225.

Kotler, P., & Armstrong, G. (2017). Principles of Marketing, New York: Pearson Education.

Leitmann, G., & Schmitendorf, W. E. (1978). Profit maximization through advertising: a nonzero sum differential game approach. IEEE Transactions on Automatic Control, 23(4), 645-650.

Libai, B., Muller, E. & Peres, R. (2009). The diffusion of services. Journal of Marketing Research, 46(2), 163-175.

Martin-Herran, G., McQuitty, S., & Sigue, S.P. (2012). Offensive versus defensive advertising: what is the optimal spending allocation?. International Journal of Research in Advertising, 29(2), 210-219.

Min, S., Zhang, X., Kim, N., & Srivastava, R. K. (2016). Customer acquisition and retention spending: an analytical model and empirical investigation in wireless telecommunications markets. Journal of Advertising Research, 53(5), 728-744.

Nair, A., & Narasimhan, R. (2006). Dynamics of competing with quality- and advertising- based goodwill. European Journal of Operational Research, 175(1), 462-474.

Nerlove, M., & Arrow, K. J. (1962). Optimal advertising policy under dynamic conditions. Economica, 29(114), 129-142.

Neslin, S. A., Gupta, S., Kamakura, W., Lu, J., & Mason, C. H. (2006). Defection detection: measuring and understanding the predictive accuracy of customer churn models. Journal of Marketing Research, 43(2), 204-211.

Nguyen, D., & Shi, L. (2006). Competitive advertising strategies and market-size dynamics: a research note on theory and evidence. Management Science, 52(6), 965-973.

Prasad, A., Sethi, S. P., & Naik, P. A. (2012). Understanding the impact of churn in dynamic oligopoly markets. Automatica, 48(11), 2882-2887.

Reichheld, F. F., & Sasser, W. E. (1990). Zero defections: quality comes to services. Harvard Business Review, 68(5), 105-111.

Reinartz, W. J., & Venkatesan, R. (2008). Decision models for customer relationship management (CRM). In B. Wierenga (Ed.), Handbook of Marketing Decision Models (pp. 291-326). Boston, MA: Springer.

Rust, R.T., & Chung, T.S. (2006). Marketing models of service and relationship. Marketing Science, 25(6), 560-580.

Rust, R. T., Lemon, K. N., & Zeithaml, V. A. (2004). Return on marketing: using customer equity to focus marketing strategy. Journal of Marketing, 68(1), 109-127.

Vidale, M. L., & Wolfe, H. B. (1957). An operations-research study of sales response to advertising. Operations Research, 5(3), 370-381.

Viscolani, B., & Zaccour, G. (2009). Advertising strategies in a differential game with negative competitor’s interference. Journal of Optimization Theory and Applications, 140(1), 153-170.

Wang, Q., & Wu, Z. (2001). A duopolistic model of dynamic competitive advertising. European Journal of Operational Research, 128(1), 213-226.

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