Percolation models of competition and monopolisation in the agricultural market

The study was relevant due to the growing risks of agricultural market monopolisation in Ukraine, which necessitated a quantitative analysis of concentration processes using modern modeling tools. The purpose of the study was to build a model of monopoly formation in the agricultural market by applying a percolation approach to forecasting phase transitions in a competitive environment. A two-dimensional percolation model of the agricultural market was developed to simulate the capture of market segments by large formations and assess concentration dynamics. Numerical experiments (200×200 domain) showed that as the control parameter approaches the critical value P* = 0.5945, the correlation coefficient of rating-frequency diagrams fell sharply from 0.94-0.97 at P = 0.50-0.58 to 0.55 at P = 0.59, indicating a phase transition interpreted as monopoly cluster formation. Using Ukrainian agricultural market data for 2017-2023, the model identified a critical percolation threshold at P* = 0.59, accompanied by a decline in correlation coefficients from 0.96 to 0.55. A logarithmic relationship W = -0.3839-0.153 ln ∣ P−P* ∣, R 2 = 0.9821 described the growth of dominant clusters. The number of agricultural enterprises declined from 40.7 to 30 thousand (-26%) and average land per enterprise increased from 490 to 576 ha, confirming the intensification of concentration processes and illustrating how geometric cluster behaviour mirrors real structural shifts in the sector, thereby strengthening the applied significance of the developed modelling approach and providing a quantitative framework for detecting early signs of market dominance, assessing systemic vulnerabilities, and interpreting concentration dynamics through the lens of phase-transition phenomena. The practical value of the study lies in enabling early identification of market monopolisation and critical transition points, thereby supporting more accurate forecasting of structural shifts and the development of effective antitrust and regulatory measures