A supply chain network game theory model of cybersecurity investments with nonlinear budget constraints

Abstract

In this paper, we develop a supply chain network game theory model consisting of retailers and demand markets with retailers competing noncooperatively in order to maximize their expected profits by determining their optimal product transactions as well as cybersecurity investments subject to nonlinear budget constraints that include the cybersecurity investment cost functions. The consumers at the demand markets reflect their preferences through the demand price functions, which depend on the product demands and on the average level of cybersecurity in the supply chain network. We identify the supply chain network vulnerability to cyberattacks as well as that of the individual retailers. We demonstrate that the governing Nash equilibrium conditions can be formulated as a variational inequality problem and we provide a novel alternative formulation, along with the accompanying theory. We also propose an algorithm for the alternative formulation, which yields, at each iteration, closed form expressions in product transactions, security levels, and Lagrange multipliers associated with the budget constraints. We then apply the algorithm to compute solutions to a spectrum of numerical supply chain network cybersecurity investment examples. The examples broaden our understanding of the impacts of the addition of retailers, changes in budgets, demand price functions, and financial damages, on equilibrium product transactions and cybersecurity investments, as well as on the supply chain network vulnerability and retailer vulnerability under budget constraints.

Cybersecurity investments with nonlinear budget constraints and conservation laws: variational equilibrium, marginal expected utilities, and Lagrange multipliers

“…() and Nagurney et al. (, ). The demand must satisfy the following conservation law: …”

“…In this paper, we consider a recently studied cybersecurity investment supply chain game theory model consisting of retailers and consumers at demand markets with each retailer being faced with a nonlinear budget constraint on their security investments (see Daniele et al., ; Nagurney et al., ). We present an alternative to this model in which the demand for the product at each demand market is known and fixed and, hence, the conservation law of each demand market must be fulfilled.…”

“…The supply chain game theory model with cybersecurity investments in the case of fixed, that is, inelastic, demands, unlike the models of Nagurney et al. () and Daniele et al. (), is characterized by a feasible set such that the strategy of a given retailer is affected by the strategies of the other retailers since the product can come from any (or all) of them.…”

“…We note that in the papers by Nagurney et al. () and Daniele et al. (), the governing Nash equilibrium conditions are formulated in terms of a variational inequality, and an analysis of the dual problem and its associated Lagrange multipliers is performed.…”

Innovative supply chain optimization models with multiple uncertainty factors

“…Supply chain network design is a popular topic in the literature (Nagurney et al 2016) and SCND under uncertainty has gained considerable attention in both practice and academia during recent years (Govindan and Fattahi 2017). Four papers fall into this area.…”