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Dynamics of Duopoly Models with Undecided Clients under Decentralized Affine Feedback Advertising Policies

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  • Walter Aliaga
  • Amit Bhaya
  • Eugenius Kaszkurewicz

Abstract

This paper extends the Deal-Vidal-Wolfe and Lanchester models of duopoly dynamics, which involve two populations, by explicitly introducing a third population of undecided users. An analysis of these extended models establishes conditions for the existence of equilibria, as well as their stability properties under different classes of advertising policies. This analysis also leads to the surprising result that the extended Vidale–Wolfe and Lanchester models, despite having different dynamics, under the general class of decentralized affine feedback advertising policies have equilibria in identical locations, with the same stability properties.

Suggested Citation

  • Walter Aliaga & Amit Bhaya & Eugenius Kaszkurewicz, 2020. "Dynamics of Duopoly Models with Undecided Clients under Decentralized Affine Feedback Advertising Policies," Complexity, Hindawi, vol. 2020, pages 1-11, January.
    • Handle: RePEc:hin:complx:5371492
    DOI: 10.1155/2020/5371492
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    Cited by:

    1. Amit Bhaya & Eugenius Kaszkurewicz, 2023. "Dynamic Advertising Games in Duopolies Under One-Step-Ahead Optimal Control," Dynamic Games and Applications, Springer, vol. 13(3), pages 721-749, September.

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