Optimal dynamic marketing-mix policies for frequently purchased products and services versus consumer durable goods: a generalized analytic approach. (English) Zbl 1430.90360
Summary: This paper deals with the qualitative characterization of optimal pricing and advertising policies together with the optimal ratio of the advertising elasticity of demand to its price elasticity over time. The problem is studied for frequently purchased products and services (FPS) as well as consumer durable goods (CDG) in both monopolistic and duopolistic markets. Demand dynamics, cost learning and discounting of future profits are taken into consideration. In addition, both the open-loop and feedback methodologies are pursued to characterize and compare the derived optimal policies. The paper uses an analytical approach to characterize the optimal dynamic policies in a general setting as is mathematically tractable, followed by the analysis of more specific models to gain additional managerial insights while maintaining a certain degree of generality. Optimal FPS marketing-mix policies are shown to be different from their CDG counterparts for both monopolistic and duopolistic markets. While the ratio of advertising elasticity to price elasticity appears to have been governed by similar set of rules for FPS and CDG, the direction of change of such ratio over time looks different from each other. Managerial implications and directions for future research are also discussed.
MSC:
| 90B60 | Marketing, advertising |
| 91A23 | Differential games (aspects of game theory) |
| 91A80 | Applications of game theory |
Keywords:
OR in marketing; marketing-mix; FPS and CDG dynamic models; maximum principle; differential gamesReferences:
| [1] | Avagyan, V.; Esteban-Bravo, M.; Vidal-Sanz, J. M., Licensing radical product innovations to speed up the diffusion, European Journal of Operational Research, 239, 2, 542-555 (2014) · Zbl 1339.91019 |
| [2] | Bass, F.; Bultez, A., A note on optimal strategic pricing of technological innovations, Marketing Science, 371-378 (1982) |
| [3] | Bass, F. M.; Krishnan, T. V.; Jain, D. C., Why the bass model fits without decision variables, Marketing Science, 13, 3, 203-223 (1994) |
| [4] | Bass, F. M., The relationship between diffusion rates, experience curves, and demand elasticities for consumer durable technological innovations, Journal of Business, 53, July, Part 2, 551-557 (1980) |
| [5] | Bimpikis, K.; Ozdaglar, A.; Yildiz, E., Competitive targeted advertising over networks, Operations Research, 64, 3, 705-720 (2016) · Zbl 1348.90366 |
| [6] | Boone, T.; Ganeshan, R.; Hicks, R. L., Learning and knowledge depreciation in professional services, Management Science, 54, 7, 1231-1236 (2008) |
| [7] | Bronnenberg, B. J.; Mahajan, V.; Vanhonacker, W. R., The emergence of market structure in new-repeat-purchase categories: The interplay of market share and retail distribution, Journal of Marketing Research, 37, 1, 16-31 (2000) |
| [8] | Chambers, S.; Johnston, R., Experience curves in services: Macro and micro level approaches, International Journal of Operations and Production Management, 20, 7, 842-859 (2000) |
| [9] | Chasparis, G. C.; Shamma, J. S., Control of preferences on social networks, (IEEE conference on decision and control (CDC) (2010)), 6651-6656 |
| [10] | Chatterjee, R.; Crosbie, P., Dynamic pricing strategies and firm performance in a duopoly: The impact of buyer expectations (1999), Katz Graduate School of Business, University of Pittsburgh: Katz Graduate School of Business, University of Pittsburgh Pittsburgh, PA, Working Paper |
| [11] | Chintagunta, P. K.; Rao, V. R., Pricing strategies in a dynamic duopoly: A differential game model, Management Science, 42, 11, 1501-1514 (1996) · Zbl 0879.90031 |
| [12] | Chintagunta, P. K.; Rao, V. R.; Vilcassim, N. J., Equilibrium pricing and advertising strategies for nondurable experience products in a dynamic duopoly, Managerial and Decision Economics, 14, 3, 221-234 (1993) |
| [13] | Chintagunta, P. K.; Vilcassim, N. J., An empirical investigation of advertising strategies in a dynamic duopoly, Management Science, 38, 9, 1230-1244 (1992) · Zbl 0775.90125 |
| [14] | Clarke, F. H.; Darrough, M. N.; Heinke, J., Optimal pricing strategies in the presence of experience effects, Journal of Business, 35, November, 517-530 (1982) |
| [15] | Deal, K.; Sethi, S. P.; Thompson, G. L., A bilinear-quadratic differential game in advertising (1978), Carnegie-Mellon University: Carnegie-Mellon University Pittsburgh, PA, Management Science Research Group · Zbl 0416.90040 |
| [16] | Deal, K. R., Optimizing advertising expenditures in a dynamic duopoly, Operations Research, 27, 4, 682-692 (1979) · Zbl 0412.90039 |
| [17] | Dockner, E., Optimal pricing in a dynamic duopoly game model, Zeitschrift für Operations Research, 29, 2, B1-B6 (1985) · Zbl 0571.90007 |
| [18] | Dockner, E.; Feichtinger, G., Dynamic advertising and pricing in an oligopoly: a Nash equilibrium approach, Dynamic games and applications in economics, 238-251 (1986), Springer: Springer Berlin, Heidelberg · Zbl 0586.90018 |
| [19] | Dockner, E.; Jørgensen, S., Optimal advertising policies for diffusion models of new product innovations in monopolistic situations, Management Science, 34, January, 119-130 (1988) |
| [20] | Dockner, E.; Jørgensen, S., Optimal pricing strategies for new products in dynamic oligopolies, Marketing Science, 7, 251-334 (1988) |
| [21] | Dockner, E. J.; Gaunersdorfer, A., Strategic new product pricing when demand obeys saturation effects, European Journal of Operational Research, 90, 3, 589-598 (1996) · Zbl 0907.90042 |
| [22] | Dockner, E. J.; Jørgensen, S., New product advertising in dynamic oligopolies, Zeitschrift für Operations Research, 36, 5, 459-473 (1992) · Zbl 0757.90042 |
| [23] | Dockner, E. J.; Jørgensen, S.; Van Long, N.; Sorger, G., Differential games in economics and management science (2000), Cambridge University Press · Zbl 0996.91001 |
| [24] | Dolan, R. J.; Jeuland, A. P., Experience curves and dynamic demand models: Implications for optimal pricing strategies, Journal of Marketing, 45, winter, 52-62 (1981) |
| [25] | Dorfman, R.; Steiner, P. O., Optimal advertising and optimal quality, American Economic Review, 4, 826-836 (1954) |
| [26] | Eliashberg, J.; Jeuland, A. P., The impact of competitive entry in a developing market upon dynamic pricing strategies, Marketing Science, 5, 1, 20-36 (1986) |
| [27] | (Eliashberg, J.; Lilien, G. L., HandhooLs in Operations Research and Management Science, Volume 5 (1993), Marketing. Amsterdam: Marketing. Amsterdam North Holland) · Zbl 0898.90001 |
| [28] | Erickson, G. M., A model of advertising competition, Journal of Marketing Research, 297-304 (1985) |
| [29] | Erickson, G. M., Advertising strategies in a dynamic oligopoly, Journal of Marketing Research, 32, 2, 233-237 (1995) |
| [30] | Erickson, G. M., Dynamic models of advertising competition (2003), Springer Science & Business Media |
| [31] | Erickson, G. M., An oligopoly model of dynamic advertising competition, European Journal of Operational Research, 197, 1, 374-388 (2009) · Zbl 1157.91316 |
| [32] | Erickson, G. M., Differential game models of advertising competition, European Journal of Operational Research, 83, 3, 431-438 (1995) · Zbl 0896.90144 |
| [33] | Feichtinger, G., Optimal pricing in a diffusion model with concave price-dependent market potential, Operations Research Letters, 1, 6, 236-240 (1982) · Zbl 0497.90040 |
| [34] | Feichtinger, G.; Dockner, E., A note to jørgensen’s logarithmic advertising differential game, Zeitschrift für Operations Research, 28, 4, B133-B153 (1984) · Zbl 0538.90043 |
| [35] | Feichtinger, G.; Jørgensen, S., Differential game models in management science, European Journal of Operational Research, 14, 2, 137-155 (1983) · Zbl 0519.90103 |
| [36] | Feinberg, F. M., On continuous-time optimal advertising under S-shaped response, Management Science, 47, 11, 1476-1487 (2001) |
| [37] | Fershtman, C., Identification of classes of differential games for which the open loop is a degenerate feedback nash equilibrium, Journal of Optimization Theory and Applications, 55, 2, 217-231 (1987) · Zbl 0616.90108 |
| [38] | Friedman, J. W., Oligopoly and the theory of games (1977), North-Holland: North-Holland Amesterdam · Zbl 0385.90001 |
| [39] | Friedman, J. W., Oligopoly theory (1983), Cambridge University Press: Cambridge University Press Cambridge |
| [40] | Fruchter, G. E.; Rao, R. C., Optimal membership fee and usage price over time for a network service, Journal of Service Research, 4, 1, 3-14 (2001) |
| [41] | Fruchter, G. E.; Sigué, S. P., Dynamic pricing of subscription services, Journal of Economic Dynamics & Control, 37, 2180-2194 (2013) · Zbl 1402.91142 |
| [42] | Fruchter, G. E.; Van den Bulte, C., Why the generalized bass model leads to odd optimal advertising policies, International Journal of Research in Marketing, 28, 3, 218-230 (2011) |
| [43] | Gupta, M. C.; Di Benedetto, C. A., Optimal pricing and advertising strategy for introducing a new business product with threat of competitive entry, Industrial Marketing Management, 36, 4, 540-548 (2007) |
| [44] | Hahn, M.; Hyun, J. S., Advertising cost interactions and the optimality of pulsing, Management Science, 37, 2, 157-169 (1991) · Zbl 0724.90036 |
| [45] | Haurie, A.; Krawczyk, J. B.; Zaccour, G., Games and dynamic games (2012), World Scientific: World Scientific Singapore · Zbl 1396.91003 |
| [46] | Helmes, K.; Schlosser, R., Oligopoly pricing and advertising in isoelastic adoption models, Dynamic Games and Applications, 5, 3, 334-360 (2015) · Zbl 1348.91205 |
| [47] | Horsky, D.; Simon, L. S., Advertising and the diffusion of new products, Marketing Science, 2, 1, 1-17 (1983) |
| [48] | Huang, J.; Leng, M.; Liang, L., Recent developments in dynamic advertising research, European Journal of Operational Research, 220, 3, 591-609 (2012) · Zbl 1253.90125 |
| [49] | Jones, J. M.; Ritz, C. J., Incorporating distribution into new product diffusion models, International Journal of Research in Marketing, 8, 2, 91-112 (1991) |
| [50] | Jørgensen, S., A survey of some differential games in advertising, Journal of Economic Dynamics and Control, 4, 341-369 (1982) |
| [51] | Jørgensen, S.; Zaccour, G., Differential games in marketing (2004), Kluwer Academic Publishers |
| [52] | Kalish, S., Monopolist pricing with dynamic demand and production cost, Marketing Science, 2, 2, 135-159 (1983) |
| [53] | Kamien, M. I.; Schwartz, N. L., Dynamic optimization (1981), North Holland: North Holland New York · Zbl 0455.49002 |
| [54] | Kamien, M. I.; Schwartz, N. L., Dynamic optimization (1991), North Holland: North Holland New York · Zbl 0727.90002 |
| [55] | Kaul, A.; Wittink, D. R., Empirical generalizations about the impact of advertising on price sensitivity and price, Marketing Science, 14, 3-supplement, G151-G160 (1995) |
| [56] | Krishnamoorthy, A.; Prasad, A.; Sethi, S. P., Optimal pricing and advertising in a durable-good duopoly, European Journal of Operational Research, 200, 2, 486-497 (2010) · Zbl 1177.90232 |
| [57] | Krishnan, T. V.; Bass, F. M.; Jain, D. C., Optimal pricing strategy for new products, Management Science, 45, December, 1650-1663 (1999) · Zbl 1231.90251 |
| [58] | Libai, B.; Muller, E.; Peres, R., The diffusion of services, Journal of Marketing Research, 46, 163-175 (2009) |
| [59] | Mahajan, V.; Muller, E.; Bass, F., Handbooks in operations research and management science, (Eliashberg, J.; Lilien, G. L. (1993)), vol. Marketing, chap. New Product Diffusion Models |
| [60] | Mahajan, V.; Muller, E.; Bass, F., New product diffusion models in marketing: A review and directions for research, Journal of Marketing, 54, 1, 1-26 (1990) |
| [61] | Mahajan, V.; Muller, E.; Wind, Y., New – product diffusion models (2000), Kluwer: Kluwer Boston, MA |
| [62] | Masucci, A. M.; Silva, A., Advertising competitions in social networks, (Proceedings of the American control conference (2017)), 4619-4624 |
| [63] | Meade, N.; Islam, T., Modeling and forecasting the diffusion of innovation- A 25 year review, International Journal of Forecasting, 22, 529-545 (2006) |
| [64] | Mesak, H. I.; Bari, A.; Babin, B. J.; Birou, L. M.; Jurkus, A., Optimum advertising policy over time for subscriber service innovations in the presence of service cost learning and customers’ disadoption, European Journal of Operational Research, 211, 3, 642-649 (2011) · Zbl 1237.90126 |
| [65] | Mesak, H. I.; Bari, A.; Blackstock, R., On the robustness and strategic implications of a parsimonious advertising – inventory competitive model with extensions to pricing competition, International Journal of Production Economics, 180, 38-47 (2016) |
| [66] | Mesak, H. I.; Clark, J. W., Monopolist optimum pricing and advertising policies for diffusion models of new product innovations, Optimal Control Applications and Methods, 19, 2, 111-136 (1998) |
| [67] | Mesak, H. I.; Darrat, A. F., Optimal pricing of new subscriber services under interdependent adoption processes, Journal of Service Research, 5, 2, 140-153 (2002) |
| [68] | Nagle, T., The strategy and tactics of pricing (1987), Prentice Hall: Prentice Hall Englewood Cliffs, NJ |
| [69] | Nerlove, M.; Arrow, K. J., Optimal advertising policy under dynamic conditions, Economica, 39, 129-142 (1962) |
| [70] | Parker, P. M., Price elasticity dynamics over the adoption life cycle, Journal of Marketing Research, 24, August, 358-367 (1992) |
| [71] | Peres, R.; Muller, E.; Mahajan, V., Innovation diffusion and new product growth models: A critical review and research directions, International Journal of Research in Marketing, 27, 2, 91-106 (2010) |
| [72] | Piconni, M. J.; Olson, C. L., Advertising decision rules in a multibrand environment: Optimal control theory and evidence, Journal of Marketing Research, 15, February, 82-92 (1979) |
| [73] | Pontryagin, L. D., The mathematical theory of optimal processes (1962), Interscience Publishers Inc: Interscience Publishers Inc New York · Zbl 0102.32001 |
| [74] | Raman, K., Boundary value problems in stochastic optimal control of advertising, Automatica, 42, 8, 1357-1362 (2006) · Zbl 1108.93081 |
| [75] | Robinson, B.; Lakhani, C., Dynamic price models for new product planning, Management Science, 10, June, 113-122 (1975) |
| [76] | Rust, R. T.; Zahorick, A. J.; Keiningham, T. L., Return of quality (ROQ): Making service quality financially accountable, Journal of Marketing, 59, April, 58-70 (1995) |
| [77] | Sasieni, M. W., Optimal advertising expenditure, Management Science, 18, 4, 64-72 (1971) |
| [78] | Schlereth, C.; Skiera, B.; Wolk, A., Measuring consumers’ preferences for metered pricing of services, Journal of Service Research, 14, 4, 443-459 (2011) |
| [79] | Seierstad, A.; Sydsaeter, K., Sufficient conditions in optimal control theory, International Economic Review, 18, 367-391 (1977) · Zbl 0392.49010 |
| [80] | Sethi, S. P., Optimal control of the vidale-wolfe advertising model, Operations Research, 21, 4, 998-1013 (1973) · Zbl 0278.49007 |
| [81] | Sethi, S. P., Optimal control of a logarithmic advertising model, Operational Research Quarterly, 26, 2(i), 317-319 (1975) · Zbl 0301.49019 |
| [82] | Sethi, S. P.; Prasad, A.; He, X., Optimal advertising and pricing in a new-product adoption model, Journal of Optimization Theory and Applications, 139, 2, 351-360 (2008) · Zbl 1159.49035 |
| [83] | Sethi, S. P.; Thompson, G. L., Optimal control theory: Applications to management science and economics (2000) · Zbl 0998.49002 |
| [84] | Teng, J. T.; Thompson, G. L., Oligopoly models for optimal advertising when production costs obey a learning curve, Management Science, 30, September, 1087-1101 (1983) · Zbl 0522.90052 |
| [85] | Teng, J. T.; Thompson, G. L., Optimal strategies for general price-advertising models, (Feichtinger, G., Optimal control theory and economic analysis 2 (1985), Elsevier: Elsevier North Holland), 183-195 · Zbl 0626.90048 |
| [86] | Thepot, J., Marketing and investment policies of duopolists in a growing industry, Journal of Economic Dynamics and Control, 5, 387-404 (1983) |
| [87] | Thompson, G. L.; Teng, J., T optimal pricing and advertising policies for new product oligopoly models, Marketing Science, 3, 148-168 (1984) |
| [88] | Van Mieghem, J. A., Price and service discrimination in queuing systems: Incentive compatibility of gcu scheduling, Management Science, 46, 8, 1249-1267 (2000) · Zbl 1232.90157 |
| [89] | Wernerfelt, B., A special case of dynamic pricing policy, Management Science, 32, 12, 1562-1566 (1986) |
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.
