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Oligopoly Pricing and Advertising in Isoelastic Adoption Models

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  • Kurt Helmes
  • Rainer Schlosser

Abstract

This paper deals with deterministic dynamic pricing and advertising differential games which are stylized models of special durable-good oligopoly markets. We analyze infinite horizon models with constant price and advertising elasticities of demand in the cases of symmetric and asymmetric firms. In particular, we consider general saturation/adoption effects. These effects are modeled as transformations of the sum of the cumulative sales of all competing firms. We specify a necessary and sufficient condition such that a unique Markovian Nash equilibrium for such games exist. For two classes of models we derive solution formulas of the optimal policies and of the value functions, and we show how to compute the evolution of the cumulative sales of each firm. The analysis of these games reveals that the existence of the Nash equilibrium relies on the possibility to separate a component, which is specific for each firm, from a [market] component, which is the same for all firms. The common factor is a function of the decreasing untapped market size. The individual factor of each firm reflects its individual market power and has an impact on equilibrium prices; each such coefficient depends on the price elasticities, unit costs, arrival rates, and discount factors of all competing companies. Formulas for these coefficients reveal how equilibrium prices depend on the number of competing firms, and how the entry or exit of a firm affects the price structure of the oligopoly. Copyright Springer Science+Business Media New York 2015

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  • Kurt Helmes & Rainer Schlosser, 2015. "Oligopoly Pricing and Advertising in Isoelastic Adoption Models," Dynamic Games and Applications, Springer, vol. 5(3), pages 334-360, September.
    • Handle: RePEc:spr:dyngam:v:5:y:2015:i:3:p:334-360
    DOI: 10.1007/s13235-014-0123-1
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    References listed on IDEAS

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    Cited by:

    1. Chenavaz, Régis Y. & Feichtinger, Gustav & Hartl, Richard F. & Kort, Peter M., 2020. "Modeling the impact of product quality on dynamic pricing and advertising policies," European Journal of Operational Research, Elsevier, vol. 284(3), pages 990-1001.
    2. Ghobadi, Somayeh Najafi- & Bagherinejad, Jafar & Taleizadeh, Ata Allah, 2021. "A two-generation new product model by considering forward-looking customers: Dynamic pricing and advertising optimization," Journal of Retailing and Consumer Services, Elsevier, vol. 63(C).
    3. Schlosser, Rainer, 2016. "Joint stochastic dynamic pricing and advertising with time-dependent demand," Journal of Economic Dynamics and Control, Elsevier, vol. 73(C), pages 439-452.
    4. Régis Chenavaz & Corina Paraschiv & Gabriel Turinici, 2021. "Dynamic Pricing of New Products in Competitive Markets: A Mean-Field Game Approach," Dynamic Games and Applications, Springer, vol. 11(3), pages 463-490, September.
    5. Schlosser, Rainer, 2015. "Dynamic pricing and advertising of perishable products with inventory holding costs," Journal of Economic Dynamics and Control, Elsevier, vol. 57(C), pages 163-181.
    6. Rainer Schlosser, 2016. "Stochastic dynamic multi-product pricing with dynamic advertising and adoption effects," Journal of Revenue and Pricing Management, Palgrave Macmillan, vol. 15(2), pages 153-169, April.
    7. Schlosser, Rainer, 2017. "Stochastic dynamic pricing and advertising in isoelastic oligopoly models," European Journal of Operational Research, Elsevier, vol. 259(3), pages 1144-1155.

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