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Operations Research, Engineering, and Cyber Security pp 117–134Cite as

Cybersecurity Investments with Nonlinear Budget Constraints: Analysis of the Marginal Expected Utilities

Part of the Springer Optimization and Its Applications book series (SOIA,volume 113)

Abstract

In this paper, we consider a recently introduced cybersecurity investment supply chain game theory model consisting of retailers and consumers at demand markets with the retailers being faced with nonlinear budget constraints on their cybersecurity investments. We construct a novel reformulation of the derived variational inequality formulation of the governing Nash equilibrium conditions. The reformulation then allows us to exploit and analyze the Lagrange multipliers associated with the bounds on the product transactions and the cybersecurity levels associated with the retailers to gain insights into the economic market forces. We provide an analysis of the marginal expected transaction utilities and of the marginal expected cybersecurity investment utilities. We then establish some stability results for the financial damages associated with a cyberattack faced by the retailers. The theoretical framework is subsequently applied to numerical examples to illustrate its applicability.

Keywords

  • Cybersecurity
  • Investments
  • Supply chains
  • Game theory
  • Nash equilibrium
  • Variational inequalities
  • Lagrange multipliers
  • Stability

MSC 2010:

  • 49K40
  • 65K10
  • 65K15
  • 90C33
  • 90C46.

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Acknowledgements

The research of the first author was partially supported by Istituto Nazionale di Alta Matematica Francesco Severi (Progetto di Ricerca GNAMPA 2015: Nuove frontiere dei problemi di equlibrio su rete: dallo sviluppo sostenibile alla dinamica dei disastri ambientali ai crimini informatici). The research of the third author was supported, in part, by the National Science Foundation under Grant No. 1551444. This support is gratefully acknowledged.

Author information

Authors and Affiliations

  1. Department of Mathematics and Computer Science, University of Catania, Catania, Italy

    Patrizia Daniele & Antonino Maugeri

  2. Isenberg School of Management, University of Massachusetts, Amherst, MA, 01003, USA

    Anna Nagurney

Authors
  1. Patrizia Daniele
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  2. Antonino Maugeri
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  3. Anna Nagurney
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Correspondence to Patrizia Daniele .

Editor information

Editors and Affiliations

  1. Department of Mathematics, Hellenic Military Academy, Vari Attikis, Greece

    Nicholas J. Daras

  2. Department of Mathematics, National Technical University of Athens, Athens, Greece

    Themistocles M. Rassias

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Daniele, P., Maugeri, A., Nagurney, A. (2017). Cybersecurity Investments with Nonlinear Budget Constraints: Analysis of the Marginal Expected Utilities. In: Daras, N., Rassias, T. (eds) Operations Research, Engineering, and Cyber Security. Springer Optimization and Its Applications, vol 113. Springer, Cham. https://doi.org/10.1007/978-3-319-51500-7_6

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