In this work we study the problem of tax evasion on a fully-connected
population. For this purpose, 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 a kinetic exchange opinion
dynamics, where the agents interact by pairs with competitive negative (with
probability $q$) and positive (with probability $1-q$) couplings, representing
agreement/disagreement between pairs of agents. In addition, we consider the
punishment rules of the Zaklan econophysics model, for which there is a
probability $p_{a}$ of an audit each agent is subject to in every period and a
length of time $k$ detected tax evaders remain honest. Our results suggest that
below the critical point $q_{c}=1/4$ of the opinion dynamics the compliance is
high, and the punishment rules have a small effect in the population. On the
other hand, for $q>q_{c}$ the tax evasion can be considerably reduced by the
enforcement mechanism. We also discuss the impact of the presence of the
undecided agents in the evolution of the system.Comment: 13 pages, 6 figures, accepted for publication in Physica