The paper addresses qualitatively an interdisciplinary subject of a socio-economic competition, its dynamics and the emergence of political conflicts, in terms of a model system composed of active particles able to develop behavioural strategies, by which they interact among each other. The key input is a concept of stochastic games. The focus is on highly improbable events (black swans) that look unpredictable and carry a massive impact (onset of criticality) while being a necessary result of a suitable modelling procedure. The major point here is to develop identification methods for premonitory signals that warn, at a sufficiently early stage, about the emergence of black swans. As a toy model, a generalization of a previous investigation by M. L. Bertotti and M. Delitala [Nonlinear Anal., Real World Appl. 9, No. 1, 183–196 (2008; Zbl 1132.91600)] of the asymptotic behaviour of social dynamics is proposed. Prospects for a more advanced mathematical analysis of such complex systems are mentioned.