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Sorger Game Under Uncertainty: Discrete Case

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Optimization Problems and Their Applications (OPTA 2018)

Part of the book series: Communications in Computer and Information Science ((CCIS,volume 871))

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Abstract

At the present time, the discrete-time models are not given enough attention. But these models are more realistic than the continuous models, because the allocation of funds is discrete. In the paper a new discrete model of optimal advertising is proposed. This model takes into account the uncertainties. These uncertainties are caused by acts of a set of the small companies. The companies’ problem is to maximize their market share taking into account the reaction of competitors. The problem is a discrete multistep optimal control problem. For this model the optimal control problem is solved explicitly. The Bellman method of dynamic programming is used to construct the guaranteed equilibrium.

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Acknowledgments

This research was supported by Act 211 Government of the Russian Federation, contract no. 02.A03.21.0011 and by Grant of the Foundation for perspective scientific researches of Chelyabinsk State University (2018).

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Authors and Affiliations

  1. South Ural State University, Chelyabinsk, Russia

    Natalia V. Adukova & Konstantin N. Kudryavtsev

  2. Chelyabinsk State University, Chelyabinsk, Russia

    Konstantin N. Kudryavtsev

Authors
  1. Natalia V. Adukova
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  2. Konstantin N. Kudryavtsev
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Corresponding author

Correspondence to Natalia V. Adukova .

Editor information

Editors and Affiliations

  1. Sobolev Institute of Mathematics SB RAS, Omsk, Russia

    Anton Eremeev

  2. Krasovsky Institute of Mathematics and Mechanics, Ekaterinburg, Russia

    Michael Khachay

  3. Sobolev Institute of Mathematics SB RAS, Novosibirsk, Russia

    Yury Kochetov

  4. Industrial and Systems Engineering, University of Florida, Gainesville, Florida, USA

    Panos Pardalos

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Adukova, N.V., Kudryavtsev, K.N. (2018). Sorger Game Under Uncertainty: Discrete Case. In: Eremeev, A., Khachay, M., Kochetov, Y., Pardalos, P. (eds) Optimization Problems and Their Applications. OPTA 2018. Communications in Computer and Information Science, vol 871. Springer, Cham. https://doi.org/10.1007/978-3-319-93800-4_17

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  • DOI: https://doi.org/10.1007/978-3-319-93800-4_17

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-93799-1

  • Online ISBN: 978-3-319-93800-4

  • eBook Packages: Computer ScienceComputer Science (R0)

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