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Estimation of Equilibria in an Advertising Game with Unknown Distribution of the Response to Advertising Efforts

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Modern Trends in Controlled Stochastic Processes:

Part of the book series: Emergence, Complexity and Computation ((ECC,volume 41))

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Abstract

We study a class of discrete-time advertising game with random responses to the advertising efforts made by a duopoly. The firms are assumed to observe the values of the random responses but they do not know their distributions. With the recorded values, firms estimate distributions and play estimated equilibrium strategies. Under suitable assumptions, we prove that the estimated equilibrium strategies converge to equilibria of the advertising game with the true distributions. Our results are numerically illustrated for specific cases.

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Acknowledgement

This work was partially supported by Consejo Nacional de Ciencia y Tecnología (CONACYT-México) under grant Ciencia Frontera 2019–87787.

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Authors and Affiliations

  1. Instituto Tecnológico de Sonora, Cd. Obregón, Sonora, Mexico

    Alan D. Robles-Aguilar

  2. CONACYT–Universidad de Sonora, Rosales s/n, 83000, Hermosillo, Sonora, Mexico

    David González-Sánchez

  3. Departamento de Matemáticas, Universidad de Sonora, Rosales s/n, 83000, Hermosillo, Sonora, Mexico

    J. Adolfo Minjárez-Sosa

Authors
  1. Alan D. Robles-Aguilar
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  2. David González-Sánchez
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  3. J. Adolfo Minjárez-Sosa
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Corresponding author

Correspondence to J. Adolfo Minjárez-Sosa .

Editor information

Editors and Affiliations

  1. Department of Mathematical Sciences, University of Liverpool, Liverpool, UK

    Alexey Piunovskiy

  2. Department of Mathematical Sciences, University of Liverpool, Liverpool, UK

    Yi Zhang

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Robles-Aguilar, A.D., González-Sánchez, D., Minjárez-Sosa, J.A. (2021). Estimation of Equilibria in an Advertising Game with Unknown Distribution of the Response to Advertising Efforts. In: Piunovskiy, A., Zhang, Y. (eds) Modern Trends in Controlled Stochastic Processes:. Emergence, Complexity and Computation, vol 41. Springer, Cham. https://doi.org/10.1007/978-3-030-76928-4_8

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  • DOI: https://doi.org/10.1007/978-3-030-76928-4_8

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-76927-7

  • Online ISBN: 978-3-030-76928-4

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