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Francisco Munoz thanks the Mediterranean Office for Youth Program by the mobility grant (MOY GRANT N + 2010/024/01) in the Program Master in Mathematics and Mathematical engineering. Juan Carlos Nuno wishes to acknowledge the European Erasmus staff mobility programmes. We are grateful to Laura Navajas for checking the English of this manuscript. We also thank the reviewers for their useful suggestions and remarks.

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Effects of inspections in small world social networks with different contagion rules

Publicado en:Physica A-Statistical Mechanics And Its Applications. 432 76-86 - 2015-08-15 432(), DOI: 10.1016/j.physa.2015.02.096

Autores: Munoz, Francisco; Carlos Nuno, Juan; Primicerio, Mario

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Resumen

We study the way the structure of social links determines the effects of random inspections on a population formed by two types of individuals, e.g. tax-payers and tax-evaders (free riders). It is assumed that inspection occur in a larger scale than the population relaxation time and, therefore, a unique initial inspection is performed on a population that is completely formed by tax-evaders. Besides, the inspected tax-evaders become tax-payers forever. The social network is modeled as a Watts-Strogatz Small World whose topology can be tuned in terms of a parameter p is an element of [0,1] from regular (p = 0) to random (p = 1). Two local contagion rules are considered: (i) a continuous one that takes the proportion of neighbors to determine the next status of an individual (node) and (ii) a discontinuous (threshold rule) that assumes a minimum number of neighbors to modify the current state. In the former case, irrespective of the inspection intensity v, the equilibrium population is always formed by tax-payers. In the mean field approach, we obtain the characteristic time of convergence as a function of v and p. For the threshold contagion rule, we show that the response of the population to the intensity of inspections v is a function of the structure of the social network p and the willingness of the individuals to change their state, r. It is shown that sharp transitions occur at critical values of v that depends on p and r. We discuss these results within the context of tax evasion and fraud where the strategies of inspection could be of major relevance. (C) 2015 Elsevier B.V. All rights reserved.

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