Cybersecurity investments with nonlinear budget constraints and conservation laws: variational equilibrium,marginal expected utilities,and Lagrange multipliers |
| |
Authors: | Gabriella Colajanni Patrizia Daniele Sofia Giuffrè Anna Nagurney |
| |
Affiliation: | 1. Department of Mathematics and Computer Science, University of Catania, Italy;2. DIIES, Mediterranea University of Reggio Calabria, Italy;3. Department of Operations and Information Management, Isenberg School of Management, University of Massachusetts, Amherst, MA, USA |
| |
Abstract: | In this paper, we propose a new cybersecurity investment supply chain game theory model, assuming that the demands for the product are known and fixed and, hence, the conservation law of each demand market is fulfilled. The model is a generalized Nash equilibrium model with nonlinear budget constraints for which we define the variational equilibrium, which provides us with a variational inequality formulation. We construct an equivalent formulation, enabling the analysis of the influence of the conservation laws and the importance of the associated Lagrange multipliers. We find that the marginal expected transaction utility of each retailer depends on this Lagrange multiplier and its sign. Finally, numerical examples with reported equilibrium product flows, cybersecurity investment levels, and Lagrange multipliers, along with individual firm vulnerability and network vulnerability, illustrate the obtained results. |
| |
Keywords: | cybersecurity investments supply chains conservation laws game theory generalized Nash equilibrium variational inequalities Lagrange multipliers |
|
|