A model of brand competition for durable goods supply chains in a dynamic framework

Document Type: Research Paper

Authors

Department of Industrial Engineering, Iran University of Science and Technology, Tehran, Iran

Abstract

Game theory is an efficient tool to represent and conceptualize the problems concerning conflict and competition. In recent years and especially for durable products, competition between domestic and foreign brands for gaining market share has received a considerable attention. This paper study electronic commerce concepts by differential game theory and introduce a novel and comprehensive model for analyzing dynamic durable goods supply chains. Manufacturer of domestic brand as leader of the game announces his wholesale price to his retailer. Then the exclusive retailers of domestic and foreign brands play a Nash differential game in choosing their optimal retail prices and advertising efforts over time. Moreover, online pricing and advertising in a direct sales channel constitute other control variables of the manufacturer. Feedback equilibrium policies for the manufacturer and the retailers are obtained by assuming a linear demand function. A case study and sensitivity analysis are carried out to provide numerical results and managerial insights. We found that there is a reverse relationship between price sensitivity of demand and optimal levels of price and advertising efforts. Increase in advertising effectiveness parameter leads to enhancement of advertising efforts in relative marketing channel, but does not have a significant effect on pricing decisions.

Keywords


Bass, F. M. (1969). A New Product Growth for Model Consumer Durables. Management Science, 15(5),
215–227. doi:10.1287/mnsc.15.5.215.
Chiang, W. K. (2012). Supply Chain Dynamics and Channel Efficiency in Durable Product Pricing and
Distribution. Manufacturing & Service Operations Management, 14(2), 327–343.
Chiang, W. K., Chhajed, D., & Hess, J. D. (2003). Direct marketing, indirect profits: A strategic analysis
of dual-channel supply-chain design. Management Science, 49(1), 1–20.
Chutani, A., & Sethi, S. P. (2012). Optimal advertising and pricing in a dynamic durable goods supply
chain. Journal of Optimization Theory and Applications, 154(2), 615–643.
Erickson, G. M. (1992). Empirical analysis of closed-loop duopoly advertising strategies. Management
Science, 38(12), 1732–1749.
Fruchter, G. E., & Tapiero, C. S. (2005). Dynamic online and offline channel pricing for heterogeneous
customers in virtual acceptance. International Game Theory Review, 7(02), 137–150.
Horsky, D., & Simon, L. S. (1983). Advertising and the Diffusion of New Products. Marketing Science,
2(1), 1–17. doi:10.1287/mksc.2.1.1.
Jia, J., & Zhang, J. (2013). Dynamic ordering and pricing strategies in a two-tier multi-generation durable
goods supply chain. International Journal of Production Economics, 144(1), 135–142.
Jørgensen, S., & Zaccour, G. (2004). Differential games in marketing. International series in quantitative
marketing. Kluwer Academic Publishers, Boston.
Krishnamoorthy, A., Prasad, A., & Sethi, S. P. (2010). Optimal pricing and advertising in a durable-good
duopoly. European Journal of Operational Research, 200(2), 486–497.
Krishnan, T. V, Bass, F. M., & Jain, D. C. (1999). Optimal pricing strategy for new products.
Management Science, 45(12), 1650–1663.

Krishnan, T. V, Bass, F. M., & Kumar, V. (2000). Impact of a late entrant on the diffusion of a new
product/service. Journal of Marketing Research, 37(2), 269–278.
Mahajan, V., Muller, E., & Bass, F. M. (1990). New product diffusion models in marketing: A review and
directions for research. The Journal of Marketing, 1–26.
Mansfield, E. (1961). Technical change and the rate of imitation. Econometrica: Journal of the
Econometric Society, 741–766.
Martín-Herrán, G., Taboubi, S., & Zaccour, G. (2005). A time-consistent open-loop Stackelberg
equilibrium of shelf-space allocation. Automatica, 41(6), 971–982.
Nerlove, M., & Arrow, K. J. (1962). Optimal Advertising Policy Under Dynamic Conditions. Economica,
29(114), 129–142.
Robinson, B., & Lakhani, C. (1975). Dynamic price models for new-product planning. Management
Science, 21(10), 1113–1122.
Rubel, O., & Zaccour, G. (2007). A differential game of a dual distribution channel. Springer.
Sayadi, M. K., & Makui, A. (2014). Optimal advertising decisions for promoting retail and online
channels in a dynamic framework. International Transactions in Operational Research, 21(5), 777–796.
Sethi, S. P. (1983). Deterministic and stochastic optimization of a dynamic advertising model. Optimal
Control Applications and Methods, 4(2), 179–184.
Sethi, S. P., & Bass, F. M. (2003). Optimal pricing in a hazard rate model of demand. Optimal Control
Applications and Methods, 24(4), 183–196.
Sethi, S. P., Prasad, A., & He, X. (2008). Optimal advertising and pricing in a new-product adoption
model. Journal of Optimization Theory and Applications, 139(2), 351–360.
Sethi, S. P., & Thompson, G. L. (2000). Optimal control theory: Applications to Management Science and
Economics. Bayesian brain: probabilistic approaches to neural … (Second Edi.). Springer Science.
Sorger, G. (1989). Competitive dynamic advertising: A modification of the case game. Journal of
Economic Dynamics and Control, 13(1), 55–80.
Thompson, G. L., & Teng, J.-T. (1984). Optimal pricing and advertising policies for new product
oligopoly models. Marketing Science, 3(2), 148–168.
Vidale, M. L., & Wolfe, H. B. (1957). An operations-research study of sales response to advertising.
Operations Research, 5(3), 370–381.

Weber, T. A. (2005). Infinite horizon optimal advertising in a market for durable goods. Optimal Control
Applications and Methods, 26(6), 307–336.