GAME THEORY IN BUSINESS: MATHEMATICAL MODELS OF INTERACTION

Abstract

The article is devoted to the analysis of the application of mathematical models of game theory in business for modeling
the interaction of economic agents, with an emphasis on competitive strategies, the behavior of companies and consumers in a
dynamic market environment. The obtained scientific results demonstrate that game theory effectively models the competitive
behavior of firms, in particular through dominant strategies and Nash equilibria, allowing the prediction of the consequences
of price wars and the breakdown of agreements, as in the classical prisoner’s dilemma. In modeling consumer behavior, the
phenomenon of conspicuous consumption is highlighted, where payoff matrices of costs and benefits show how social effects
influence choice, shaping zero-sum games and mixed strategies to minimize losses. In marketing decisions, illustrated by the
example of the air conditioning systems market, payoff matrices with correction coefficients make it possible to determine
optimal combinations of strategies, such as network expansion or advertising campaigns, taking into account the absence of
saddle points and the transition to probabilistic profiles. The Cournot model illustrates the dynamics of a duopoly, where
cooperative strategies provide higher profits, but competitive incentives lead to defection, emphasizing the need for coordination
games for sustainable development. The practical value of the study lies in providing tools for business management, particularly
for optimizing strategies in marketing, logistics, and pricing, which helps companies minimize risks under competition and
increase profitability. The application of the proposed models allows forecasting the reactions of competitors and consumers,
contributing to effective decision-making in real market situations such as retail trade or supply chains.