Bilinear Differential Quality Games in Economic Confrontation: Optimal Strategies Under Shock Controls

The relevance of this study stems from the need for a rational allocation of limited financial resources under conditions of intense economic confrontation. The central research question is as follows: how can resources be allocated optimally and zones of guaranteed survival be mathematically justified in a continuous conflict characterized by bilinear dynamics and nonmeasurable shock controls? To address this question, we propose a new computational approach based on a differential game of quality. Unlike existing models focused primarily on abstract equilibrium analysis, the present study applies a limit-transition method for multistep positional strategies to a macroeconomic survival problem. The computational experiments explicitly construct and visualize the preference regions, i.e., the guaranteed-survival regions, of the opposing parties. Sensitivity analysis reveals an important pattern: a linear increase in the parameter α by 10% expands the system’s survival region by 14%. In addition, the proposed semi-implicit method reduces the computational time by 35–40% while preserving numerical stability. The practical significance of this study lies in establishing an algorithmic foundation for decision support systems (DSS) that can model the boundaries of economic resilience and synthesize optimal strategies for keeping the system within a safe region.