Nonequilibrium phase transitions in a model of tax evasion dynamics

The agent-based modeling of social interactions is one of the most interesting problems in statistical physics and it has been extensively explored due to its high degree of applicability (opinion dynamics, spreading of diseases, systems with competing dynamics, rumor spreading, etc). Its results are also very important from the point of view of an organized society (stationary behavior of a disease, epidemic cycles, predominance of a certain political position and many others).

In this work, we study the tax evasion dynamics in a artificial society. In this case, we consider three types of individuals in relation to tax compliance: honest, tax evaders and undecided individuals. We analyze the social interactions that may occur among these individuals and autonomous decisions, and we consider our population as a fully-connected network of $N$ nodes, that characterize a mean-field-like approach. Through analytical and numerical results, we found that even if initially there are no tax evaders in the population, these individuals may emerge in the society, and its fraction may stabilize in the population, depending on certain socio-economic parameters (efficiency of the influence of certain individuals over others, autonomous decisions, punishment rules, etc). We show that this emergency of tax evaders is associated with a nonequilibrium phase transition.