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Leader–Follower Dynamic Game of New Product Diffusion

Author

Listed:
  • M. Breton

    (GÉRAD, École des Hautes Études Commerciales)

  • F. Chauny

    (GÉRAD, École des Hautes Études Commerciales)

  • G. Zaccour

    (GÉRAD, École des Hautes Études Commerciales)

Abstract

The objective of this paper is to study optimal pricing strategies in a duopoly, under an asymmetric information structure, where the appropriate solution concept is the feedback Stackelberg equilibrium. In order to take into account effects such as imitation (e.g., word of mouth) and saturation, the demand (state equation) is assumed to depend on past cumulative sales, market potential, and both players' prices. We assume also that the unit production cost decreases with cumulative production (learning effects). Each player maximizes his total discounted profit over the planning horizon. The problem is formulated as a two-player discrete-time finite-horizon game. Existence results are first obtained under rather mild conditions. Since the solution of this problem is intractable by analytical methods, we use a numerical approach. Thus, we design a numerical algorithm for the computation of feedback Stackelberg equilibria and use it to obtain strategies in various representative cases. The numerical results presented are intented to give some insights into the optimal pricing strategies in the context of an asymmetrical feedback information structure.

Suggested Citation

  • M. Breton & F. Chauny & G. Zaccour, 1997. "Leader–Follower Dynamic Game of New Product Diffusion," Journal of Optimization Theory and Applications, Springer, vol. 92(1), pages 77-98, January.
    • Handle: RePEc:spr:joptap:v:92:y:1997:i:1:d:10.1023_a:1022636029501
    DOI: 10.1023/A:1022636029501
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    References listed on IDEAS

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    1. Shlomo Kalish, 1983. "Monopolist Pricing with Dynamic Demand and Production Cost," Marketing Science, INFORMS, vol. 2(2), pages 135-159.
    2. Engelbert Dockner & Steffen Jørgensen, 1988. "Optimal Advertising Policies for Diffusion Models of New Product Innovation in Monopolistic Situations," Management Science, INFORMS, vol. 34(1), pages 119-130, January.
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    Cited by:

    1. Nawel Amrouche & Guiomar Martín-Herrán & Georges Zaccour, 2008. "Feedback Stackelberg equilibrium strategies when the private label competes with the national brand," Annals of Operations Research, Springer, vol. 164(1), pages 79-95, November.
    2. Chaab, Jafar & Zaccour, Georges, 2024. "Dynamic pricing in the presence of social externalities and reference-price effect," Omega, Elsevier, vol. 122(C).

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