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, w e consider the punishment rules of the Zaklan econophysics model, fo r 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. 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 P a .
KeywordsEconophysicsSociophysicsMajority VoteIsing Model
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