This paper is devoted to development of the model [6] formulated in 2005, which allows to investigate the effect that inequality has on characteristics of agents’ memory. These agents strive to preserve two resources that are meaningful for agents’ existence. Agents are differentiated by basic strategies aimed to conserve one of the two resources - either tangible or intangible (i.e. linked to status, professionalism). These strategies are associated with domination of one of the two parencephalons of agent’s brain. Agents’ interaction is described by virtue of rules identified within the theory of reflexive systems by V. Lefebvre. The analysis of critical events in systems of agents of various types is conducted using the estimate for the degree of ultrametricity among agents’ histories set. The degree of inequality for the supply of tangible resource is described with effective temperature, allowing to apply methods of quantum statistics and low temperature physics (with low temperatures corresponding to pronounced inequality). The model can be potentially applied in many areas - from social to control, memory, and medical studies. The arguments explaining why the degree of ultrametricity enables to detect complementarity of the two incomplete encodings for agents’ histories under low temperatures are presented for the first time. Moreover, it is shown for the first time that model’s properties revealed previously, which are reflected in emergence of specific memory encodings as a result of exceedance of a critical value for the degree of inequality in the case of fully connected network of agents’ relations, remain unchanged in the case of agents’ networks with random connections.