Everyone on this planet is now more reliant on information and communication technology. Cybersecurity does the protection from theft and damage of all categories of data that require to be retained top secret. Cybersecurity-related problems that are predicted on lingual data have become the center of attention for researchers in modern times. It is possible to design these uncertain problems by matrix game, where the respective attacker and defender are possibly interpreted as players. Interval-valued neutrosophic numbers (IVNNs) are used as an excellent tool to counter such uncertain circumstances in respect of fuzzy sets/intuitionistic fuzzy sets or ordinary intervals. IVNN addresses topics with a set of interval numbers in the real unit interval. In this paper, cybersecurity-related issues are explored using matrix game, where the respective payoffs are considered as IVNNs. A nonlinear programming approach is presented by constructing two interval-valued multi-objective problems for the players. Then, the subsequent problems are transferred into a pair of auxiliary nonlinear programming models. The weighted average approach is used to solve the reduced problems. A numerical example of the cybersecurity problem in the banking sector is illustrated to show the applicability of the proposed approach. A comparison analysis is performed with existing work to authenticate the feasibility of the proposed approach.