TITLE:
Tax Evasion Dynamics via Ising Model Spin S = 1
AUTHORS:
F. W. S. Lima
KEYWORDS:
Econophysics, Sociophysics, Majority Vote, Ising Model
JOURNAL NAME:
Theoretical Economics Letters,
Vol.12 No.2,
March
31,
2022
ABSTRACT: In
this work, we study the problem of tax evasion on Erdös Rènyi
random graphs. Here, we consider that the agents may be in three different
states, namely honest tax payers, tax evaders, and undecided that are
individuals in an intermediate class among
honests and evaders. Every individual can change his/her state following
an Ising model dynamics with spin S =
1. In addition, we consider the punishment
rules of the Zaklan econophysics model, for which there is a probability Pa of an audit each agent
is subject to in every period and a length of time k detected tax evaders remain honest. The dynamic of temporal
evolution of the Zaklan model was studied initially via the equilibrium Ising
model with two opinions (-1 and +1), and recently via a
non-equilibrium three-state kinetic agent-based model on a fully-connected
population. Here, through Monte Carlo simulations, we study the problem of the
tax evasion fluctuations using an Ising model with spin S = 1 (-1, 0, and +1) on Erdös Rènyi
random graphs in the dynamic of the temporal evolution of the Zaklan model.
Then, we found that the Ising model with spin S = 1 is as efficient as the Ising model and non-equilibrium
three-state kinetic agent-based model in controlling the tax evasion
fluctuations. This control is even better when we use strong punishment values k even for low audit probabilities Pa.