A simple mechanism leading to first-order phase transitions in a model of tax evasion

TL;DR

This paper models tax evasion dynamics in a population, revealing that the emergence of evaders involves a first-order phase transition between active and absorbing states, influenced by social interactions and government enforcement.

Contribution

It introduces a contagion model with probabilistic transitions among honest taxpayers, evaders, and susceptibles, demonstrating a first-order phase transition in tax evasion behavior.

Findings

Tax evasion emergence is linked to a first-order phase transition.

Active phase features coexistence of all three subpopulations.

Absorbing phase results in only honest taxpayers surviving.

Abstract

In this work we study a dynamics of tax evasion. We considered a fully-connected population divided in three compartments, namely honest tax payers, tax evaders and susceptibles, a class that is composed by honest tax payers that can become evaders. We consider a contagion model where the transitions among the compartments are governed by probabilities. Such probabilities represent the possible interactions among the indiviudals, as well as the government's fiscalization. We show by analytical and numerical calculations that the emergence of tax evaders in the population is associated with an active-absorbing nonequilibrium first-order phase transition. In the absorbing phase only honest tax payers survive in the steady states of the model, and we observe a coexistence of the three subpopulations in the active phase.