Modeling competing artificial intelligence systems for energy and users

The article addresses the problem of modeling competition between two artificial intelligence systems (AI-1 and AI-2) that interact within a shared environment under limited resources such as users and energy. The study focuses on analyzing the strategic behavior and adaptability of these systems, as well as their impact on competitive outcomes through mathematical models and methods, including differential equations, the Lancaster model, and Boyd cycles (OODA-loop). Special attention is given to formalizing the interaction of systems using basic primitives ("Condition," "Loop," "Function") and their compositions, enabling the description of complex behavioral strategies of AI systems. The paper presents a detailed mathematical formalization of the dynamics of user and energy distribution between systems, taking into account factors such as user satisfaction, response accuracy, query processing speed, and energy efficiency. The research also includes numerical calculations and simulations demonstrating how initial conditions and system parameters influence competitiveness. The proposed models can be applied for predicting AI system behavior in real-world scenarios such as information campaigns, cyber conflicts, and resource optimization in digital environments.