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Pricing Strategies in a Dynamic Duopoly: A Differential Game Model

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Listed:
  • Pradeep K. Chintagunta

    (Graduate School of Business, University of Chicago, Chicago, Illinois 60637)

  • Vithala R. Rao

    (Samuel Curtis Johnson Graduate School of Management, Cornell University, Malott Hall, Ithaca, New York 14853)

Abstract

We formulate a differential game model for dynamic pricing in a duopolistic market. Firms' demand functions are derived from utility maximizing behavior of consumers with the demand for a brand given by the logit model. Preferences for brands are assumed to evolve over time in the market in a manner akin to learning models postulated in the marketing literature. We derive the differential equations governing the equilibrium open-loop price paths over time and show that in steady state, the brand with the higher preference level charges the higher price. The formulation is extended to include the effects of consumer heterogeneity, and equilibrium steady-state prices are compared with those obtained when heterogeneity is ignored. A comparison of steady-state dynamic prices with myopic prices is provided. An empirical example is discussed to show how steady-state model predictions may be obtained from actual longitudinal purchase data.

Suggested Citation

  • Pradeep K. Chintagunta & Vithala R. Rao, 1996. "Pricing Strategies in a Dynamic Duopoly: A Differential Game Model," Management Science, INFORMS, vol. 42(11), pages 1501-1514, November.
  • Handle: RePEc:inm:ormnsc:v:42:y:1996:i:11:p:1501-1514
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    File URL: http://dx.doi.org/10.1287/mnsc.42.11.1501
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    Citations

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    Cited by:

    1. Martín-Herrán, Guiomar & Taboubi, Sihem & Zaccour, Georges, 2012. "Dual role of price and myopia in a marketing channel," European Journal of Operational Research, Elsevier, vol. 219(2), pages 284-295.
    2. Liberali, Guilherme & Gruca, Thomas S. & Nique, Walter M., 2011. "The effects of sensitization and habituation in durable goods markets," European Journal of Operational Research, Elsevier, vol. 212(2), pages 398-410, July.
    3. Zhao, Li & Tian, Peng & Xiangyong Li, 2012. "Dynamic pricing in the presence of consumer inertia," Omega, Elsevier, vol. 40(2), pages 137-148, April.
    4. Vidal-Sanz, Jose M. & Mela, Carl F. & Gupta, Sunil, 2009. "The value of a "free" customer," DEE - Working Papers. Business Economics. WB wb092903, Universidad Carlos III de Madrid. Departamento de Economía de la Empresa.
    5. P. B. Seetharaman & Hai Che, 2009. "Price Competition in Markets with Consumer Variety Seeking," Marketing Science, INFORMS, vol. 28(3), pages 516-525, 05-06.
    6. Ed Hopkins, 2002. "Adaptive Learning Models of Consumer Behaviour (first version)," ESE Discussion Papers 80, Edinburgh School of Economics, University of Edinburgh.
    7. 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.
    8. Hopkins, Ed, 2007. "Adaptive learning models of consumer behavior," Journal of Economic Behavior & Organization, Elsevier, vol. 64(3-4), pages 348-368.
    9. Kalyan Talluri & Victor Martínez-de-Albéniz, 2010. "Dynamic Price Competition with Fixed Capacities," Working Papers 425, Barcelona Graduate School of Economics.
    10. Lu, Jye-Chyi & Tsao, Yu-Chung & Charoensiriwath, Chayakrit & Dong, Ming, 2012. "Dynamic decision-making in a two-stage supply chain with repeated transactions," International Journal of Production Economics, Elsevier, vol. 137(2), pages 211-225.
    11. Richards, Timothy J. & Patterson, Paul M., 2006. "Firm-Level Competition in Price and Variety," Journal of Agricultural and Applied Economics, Southern Agricultural Economics Association, vol. 0(Number 3), pages 1-22, December.
    12. Eric Anderson & Nanda Kumar, 2007. "Price competition with repeat, loyal buyers," Quantitative Marketing and Economics (QME), Springer, vol. 5(4), pages 333-359, December.
    13. Nair, Anand & Narasimhan, Ram, 2006. "Dynamics of competing with quality- and advertising-based goodwill," European Journal of Operational Research, Elsevier, vol. 175(1), pages 462-474, November.
    14. David Besanko & Sachin Gupta & Dipak Jain, 1998. "Logit Demand Estimation Under Competitive Pricing Behavior: An Equilibrium Framework," Management Science, INFORMS, vol. 44(11-Part-1), pages 1533-1547, November.
    15. Kalyan Talluri & Víctor Martínez de Albéniz, 2010. "Dynamic price competition with fixed capacities," Economics Working Papers 1205, Department of Economics and Business, Universitat Pompeu Fabra.
    16. Yuri Levin & Jeff McGill & Mikhail Nediak, 2009. "Dynamic Pricing in the Presence of Strategic Consumers and Oligopolistic Competition," Management Science, INFORMS, vol. 55(1), pages 32-46, January.
    17. Mak, Vincent & Rapoport, Amnon & Gisches, Eyran J., 2012. "Competitive dynamic pricing with alternating offers: Theory and experiment," Games and Economic Behavior, Elsevier, vol. 75(1), pages 250-264.
    18. Benchekroun, Hassan & Martín-Herrán, Guiomar & Taboubi, Sihem, 2009. "Could myopic pricing be a strategic choice in marketing channels? A game theoretic analysis," Journal of Economic Dynamics and Control, Elsevier, vol. 33(9), pages 1699-1718, September.
    19. Richards, Timothy J., 2002. "Dynamic Strategic Interaction: A Synthesis Of Modeling Methods," Western Economics Forum, Western Agricultural Economics Association, vol. 0(Number 1), pages 1-5.

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