MODEL OF ECONOMIC CONFRONTATION WITHIN THE FRAMEWORK OF DIFFERENTIAL GAMES OF QUALITY

Abstract

This article develops and investigates a multi-factor mathematical model of economic confrontation, built on the principles of differential games of quality, which are classified as games of survival. The relevance of the study is driven by the current tense international situation, where the economic component of conflicts plays a critical role in achieving strategic outcomes. The authors propose an approach where the state of each economy is described as an n -dimensional (for the first player) and m -dimensional (for the second player) vector of product values in a broad sense: ranging from industrial and agricultural goods to weaponry and financial instruments. The dynamics of the conflict are formalized through a system of bilinear differential equations that account for the growth or decline rates of economic indicators ( ), matrices of internal technological transformations ( ), and coefficients of mutual influence between the parties ( ). Particular attention is paid to the strategic management of resources: players select a portion of assets to influence the opponent (e.g., the military sphere), forcing the other side to allocate additional resources to neutralize these actions. Within the framework of a positional differential game, conditions for concluding the confrontation are defined, including the victory of one of the parties, mutual defeat, or the continuation of the struggle. The solution to the problem enabled the identification of the players' advantage sets and their optimal strategies. The practical significance of the model is confirmed by a series of computational experiments conducted in the PyCharm (Anaconda) software environment using an Intel i7 processor. The simulation results visualize conflict trajectories and can serve as a mathematical core for decision support systems (DSS) in the fields of economic security forecasting and competitiveness assessment for e-commerce entities. The proposed approach opens prospects for analyzing complex conflict situations while considering information asymmetry between the parties.

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