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

P. Daniele, A. Maugeri, A. Nagurney,
Operations Research, Engineering, and Cyber Security: Trends in Applied Mathematics and Technology, Vol. 113, Springer Optimization and Its Applications, N.J. Daras and T.M. Rassias Editors, 2017, 117-134.

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.

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