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

Francisco Muñoz, Juan Carlos Nuño and Mario Primicerio

Physica A: Statistical Mechanics and its Applications, 2015, vol. 432, issue C, 76-86

Abstract: 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 inspections 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∈[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 ν, 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 ν and p. For the threshold contagion rule, we show that the response of the population to the intensity of inspections ν 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 ν 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.

Keywords: Tax-evasion; Social network; Mathematical model; Computer simulations (search for similar items in EconPapers)
Date: 2015
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Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:432:y:2015:i:c:p:76-86

DOI: 10.1016/j.physa.2015.02.096

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