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Optimal Pricing Strategies for New Products in Dynamic Oligopolies


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  • Engelbert Dockner

    (University of Saskatchewan)

  • Steffen Jørgensen

    (Odense University)

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    This paper deals with the determination of optimal pricing policies for firms in oligopolistic markets. The problem is studied as a differential game and optimal pricing policies are established as Nash open-loop controls. Cost learning effects are assumed such that unit costs are decreasing with cumulative output. Discounting of future profits is also taken into consideration. Initially, the problem is addressed in a general framework, and we proceed to study some specific cases that are related to models presented in recent literature. Three basic classes of sales dynamics are analyzed: competition with price effects only, competition with price as well as adoption effects, and competition with adoption effects only. In some cases it turns out that results which hold for the monopoly case, carry over to the multi-firm case, in the sense that the qualitative structure of optimal pricing strategies is the same in the monopoly and the oligopoly cases. However, due to competitive interdependencies, differences certainly exist in the levels as well as the rates of change of optimal prices.

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    Bibliographic Info

    Article provided by INFORMS in its journal Marketing Science.

    Volume (Year): 7 (1988)
    Issue (Month): 4 ()
    Pages: 315-334

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    Handle: RePEc:inm:ormksc:v:7:y:1988:i:4:p:315-334

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    Keywords: dynamic pricing; oligopoly; learning curve; differential games; open-loop Nash equilibria;


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    Cited by:
    1. Teng, Jinn-Tsair & Thompson, Gerald L., 1996. "Optimal strategies for general price-quality decision models of new products with learning production costs," European Journal of Operational Research, Elsevier, vol. 93(3), pages 476-489, September.
    2. Wilhelm, Wilbert E. & Xu, Kaihong, 2002. "Prescribing product upgrades, prices and production levels over time in a stochastic environment," European Journal of Operational Research, Elsevier, vol. 138(3), pages 601-621, May.
    3. Vardan Avagyan & Mercedes Esteban Bravo & Jose Vidal-Sanz, 2011. "Riding successive product diffusion waves :building a tsunami via upgrade-rebate programs," Business Economics Working Papers wb114011, Universidad Carlos III, Departamento de Economía de la Empresa.
    4. Richards, Timothy J. & Patterson, Paul M., 2002. "Strategic Interaction With Multiple Tools: A New Empirical Model," Working Papers 28545, Arizona State University, Morrison School of Agribusiness and Resource Management.
    5. Rubel, Olivier, 2013. "Stochastic competitive entries and dynamic pricing," European Journal of Operational Research, Elsevier, vol. 231(2), pages 381-392.
    6. Jorgensen, Steffen & Zaccour, Georges, 1999. "Price subsidies and guaranteed buys of a new technology," European Journal of Operational Research, Elsevier, vol. 114(2), pages 338-345, April.
    7. Kort, P.M. & Jorgensen, S. & Zaccour, A., 1999. "Production, inventory and pricing under cost and demand learning effects," Open Access publications from Tilburg University urn:nbn:nl:ui:12-80097, Tilburg University.
    8. Vardan Avagyan & Mercedes Esteban Bravo & Jose Vidal-Sanz, 2011. "Licensing radical product innovations to speed up the diffusion," Business Economics Working Papers wb113609, Universidad Carlos III, Departamento de Economía de la Empresa.
    9. Martin Hewing, 2012. "A Theoretical and Empirical Comparison of Innovation Diffusion Models Applying Data from the Software Industry," Journal of the Knowledge Economy, Springer, vol. 3(2), pages 125-141, June.
    10. Jun, Duk B. & Kim, Seon K. & Park, Yoon S. & Park, Myoung H. & Wilson, Amy R., 2002. "Forecasting telecommunication service subscribers in substitutive and competitive environments," International Journal of Forecasting, Elsevier, vol. 18(4), pages 561-581.
    11. Lin, Pei-Chun, 2008. "Optimal pricing, production rate, and quality under learning effects," Journal of Business Research, Elsevier, vol. 61(11), pages 1152-1159, November.
    12. Awi Federgruen & Joern Meissner, 2004. "Competition under Time-Varying Demands and Dynamic Lot-Sizing Costs," Working Papers MRG/0003, Department of Management Science, Lancaster University, revised May 2008.
    13. Mesak, Hani I. & Bari, Abdullahel & Babin, Barry J. & Birou, Laura M. & Jurkus, Anthony, 2011. "Optimum advertising policy over time for subscriber service innovations in the presence of service cost learning and customers' disadoption," European Journal of Operational Research, Elsevier, vol. 211(3), pages 642-649, June.
    14. Jørgensen, Steffen & Kort, Peter M. & Zaccour, Georges, 2009. "Optimal pricing and advertising policies for an entertainment event," Journal of Economic Dynamics and Control, Elsevier, vol. 33(3), pages 583-596, March.
    15. Dockner, Engelbert J. & Gaunersdorfer, Andrea, 1996. "Strategic new product pricing when demand obeys saturation effects," European Journal of Operational Research, Elsevier, vol. 90(3), pages 589-598, May.


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