1.1 Introduction

While the formal study of tax evasion began with a seminal paper by M.G. Allingham and A. Sandmo titled “Income Tax Evasion: A Theoretical Analysis” in 1972, scholars and practitioners continue to be challenged with designing and implementing policies and incentives to mitigate tax evasion. While early theoretical studies provide a baseline from which to evaluate hypotheses, the methodology underlying the classical formulation; that is, the use of utility functions and the assumptions of taxpayer homogeneity and rationality, fall short in characterizing taxpayer behaviors observed in practice. In this book, we seek to advance the state of the art in the study of tax evasion by presenting an alternative computational approach based on simulating individual agents. These so-called agent-based models (ABM) aim to take into account individual preferences and can accommodate a larger variety of intrinsic and extrinsic variables to help explore a broader space of compliance outcomes. In this introductory chapter, we present a formal definition of tax evasion in Section 1.2 and outline the case for why its analysis is a priority not only for tax administrators, but also for society at large. The classical theoretical models of tax evasion are then summarized in Section 1.3 to provide historical context as well as an understanding of the assumptions and abstractions that have helped formalize the preliminary studies in this field. The ABM paradigm is introduced in Section 1.4 with an outline of the Overview, Design Concepts, and Details plus Decision-Making (ODD+D) protocol (Müller et al., 2013) that we propose as a standard to guide both the development and presentation of simulation results. Here we stress the need to calibrate and replicate ABMs to help further advance our collective efforts. A literature review follows in Section 1.6 describing the tax evasion agent-based methods developed to date. In conclusion, Section 1.7 provides an overview of the edited volume by summarizing the remaining chapters that further explore the nuances in this field.

1.2 Tax Evasion, Tax Avoidance and Tax Noncompliance

What constitutes tax evasion? Alm (2012, p. 55) defines tax evasion as the “illegal and intentional actions taken by individuals to reduce their legally due tax obligations.” The most common “strategies” for tax evasion involve intentionally underreporting income, claiming fake deductions and credits, exploiting loopholes in the tax regulations, and engineering artificial losses. The US Internal Revenue Service (IRS) links tax evasion with tax fraud, which it defines as “an intentional wrongdoing, on the part of the taxpayer, with the specific purpose of evading a tax known or believed to be owing” (IRS, 2016b). Note that tax evasion should be distinguished from legal tax avoidance that allows individuals to reduce their tax liability through legitimate means. A grey area exists when individuals exploit tax loopholes as a means for tax avoidance. In certain countries (such as Germany) this may fall within the definition of legal tax avoidance. Notably, Slemrod and Yitzhaki (2002) distinguish tax avoidance and evasion, where the former is the legal usage of tax loopholes to lower the tax burden while the later is illegal. Thus the law draws the line between tax avoidance and evasion.

An additional term “tax noncompliance” also appears in the literature and is sometimes used interchangeably with tax evasion. We consider tax noncompliance as a more general term that includes both intentional evasion and unintentional errors. However, the tax gap studies by the IRS reports overall tax noncompliance (estimated at $458 billion for 2008–2010, see IRS, 2016a) without attempting to consider this distinction (GAO, 2012, p. 3). Hence, strictly speaking, interchangeable use of tax evasion and tax noncompliance is inconsistent. To be clear, our discussions center on characterizing intentional acts by individuals to reduce their tax liability rather than on factors that may lead to mistakes in tax reporting.

One may ask, why analyze tax evasion? First and foremost, tax is essential to fund public expenditures. Tax evasion is therefore not only a concern for the tax authorities, but also for society at large. Given a nation's investment in healthcare, education, defence, social security, transportation, infrastructure, science and technology are derived substantially from public financing, tax evasion causes misallocations of public goods (Andreoni et al., 1998; Slemrod and Yitzhaki, 2002; Torgler, 2002; Kirchler, 2007; Slemrod, 2007; Alm, 2012, provide surveys, and James and Edwards, 2010, present a bibliography of the literature on tax compliance). Moreover, given the nonnegligible extent of tax evasion as indicated by the tax gap estimates by the IRS (2016a), tax authorities can incur significant expenses to enact deterrence efforts. An analysis of tax evasion can therefore be used to identify factors that influence compliance rates and ultimately help governments reach revenue targets. Secondly, by exploring issues of tax evasion across different tax systems, there is an opportunity to inform and share insight about the effectiveness of different policy initiatives. As an example, even though the tax rate, tax base, and tax-exempt amounts may differ among nations, cross-border comparison of countries with flat income taxes might yield valuable lessons. Now that we have briefly discussed the meaning of terms used to describe tax evasion, tax avoidance, and tax noncompliance, we will now address theories of tax evasion.

1.3 Standard Theories of Tax Evasion

Research on tax evasion started in the 1970s with the seminal works by Allingham and Sandmo (1972) and Srinivasan (1973), who applied the economics-of-crime approach by Becker (1968, 1993) to tax reporting behavior.¹ Comparing these tax reporting models reveals various distinctions and similarities, that can be grouped based on (i) mathematical modeling, (ii) taxpayer's optimal choice, (iii) comparative statics, (iv) framework extensions, and (v) model critique.

To begin with, we briefly describe standard versions of the tax evasion models. Allingham and Sandmo (1972) consider an individual, a taxpayer, who is faced by a decision problem about how much income of the true income to declare to the tax authority given an audit probability , a tax rate , and a penalty rate . Further, the taxpayer is assumed to be risk averse, so that the marginal utility is strictly decreasing;, that is, the resulting utility function is concave. To solve the decision problem, the taxpayer maximizes his expected utility

1.1

such that the necessary condition for a maximum is

1.2

The taxpayer has an incentive toward tax evasion if his marginal expected utility is positive for total evasion, that is, , and negative for full tax compliance, that is, ; mathematically speaking the first derivative of the expected utility with respect to income declaration needs to have a sign change, and the second derivative must be negative. The latter condition is fulfilled because of the concavity of the utility function and the former condition leads to

1.3

and

1.4

Rearranging Eqs (1.3) and (1.4), yields the condition which guarantees an interior solution for the income maximization problem

1.5

If the tax rate changes, then a fixed penalty rate on undeclared income might cause a conflict between two effects on the optimal income declared : an income effect and a substitution effect. Yitzhaki (1974) shows that modeling a fine on the evaded tax via a sanction tax rate resolves this conflict.

Implicitly assuming a linear utility function, Srinivasan (1973) investigates the taxpayer's expected income after taxes and penalties

1.6

where denotes the taxes as function of true income, and the penalties as function of denoting the fraction of true income not declared to the tax authority. Hence, the first-order condition for a maximum is

1.7

Mathematical syntax	Meaning
	Audit probability
	Tax rate
	Penalty rate
	Sanction tax rate
	Fraction of true income not declared to the tax authority
	True income
	Income declaration
	Optimal income declaration
	Utility
	Marginal utility
	Expected utility
	Expected income (after tax and penalties)
	Tax function
	Punishment function

Table 1.1 summarizes the mathematical syntax and its meaning in these standard tax reporting theories. The essential distinction in the tax evasion theories is that Allingham and Sandmo (1972) employ expected utility maximization while Srinivasan (1973) maximizes an expected income after tax and penalties without an utility function modeled explicitly. The strict concavity of the utility functions permits Allingham and Sandmo (1972) to explore the tax reporting behavior of risk averse taxpayers. In particular, Allingham and Sandmo (1972) rule out linear utility functions because of the need for a strict decline of marginal utility. To put it differently, Allingham and Sandmo (1972) provide an all-or-nothing solution for the borderline case of a linear utility function, that is, a risk neutral individual. Yet, risk neutral subjects are implicitly considered by Srinivasan (1973).² Furthermore, taxpayers considered in the Allingham and Sandmo (1972) model chose an optimal amount of the income to declare while Srinivasan (1973) assumes the taxpayers to declare an optimal fraction understating the income. Both models suppose taxpayers can report between the true value, that is, full tax compliance, and nothing that is, full tax evasion. A fixed audit probability is the standard assumption in Allingham and Sandmo (1972). Thus, Srinivasan (1973) represents a broader framework in the sense of implementing an audit probability, which varies and may depend on income declaration. Srinivasan (1973) makes use of progressive tax schemes without any kind of tax allowances or deductions while the fixed tax rate in Allingham and Sandmo (1972) reflects a flat tax scenario. Further, a taxpayer faces a fixed penalty rate on nondeclared income if his cheating behavior is uncovered. Srinivasan (1973) varies a penalty rate on nondeclared income. To summarize, the mathematical features in Allingham and Sandmo (1972) and Srinivasan (1973) are quite similar but differ with respect to optimization procedures, perceived taxpayer's risk attitudes, decision variables, audit probabilities, tax tariffs, and penalty functions.

Second, to find the taxpayer's optimal reporting behavior both theories of tax evasion take into account a first-order condition, which refers either to maximizing the expected utility (Allingham and Sandmo, 1972) or the expected income after tax and penalties (Srinivasan, 1973). Allingham and Sandmo (1972) derive taxpayer's evading conditions (Eq. (1.5)) when to declare no income at all, full income or a fraction of true income, that is, an interior solution. The Allingham and Sandmo (1972) conditions (Eq. (1.5)) depend on the characteristics of taxpayer's utility function and the “tax enforcement variables,” audit probability, penalty, and tax rate (e.g., see Cowell, 1992, p. 527). The interior solution vanishes if taxpayer's utility function reflects risk neutrality. Likewise, Srinivasan (1973) proves the existence of an interior solution depending on audit probability and the characteristics of prevailing tax and penalty functions. It is remarkable that this study does not allow for a corner solution, which is quite a converse result to Allingham and Sandmo (1972).

Third, while comparative statics bring up a variety of findings, both tax evasion models show a coinciding result; that is, increasing the audit probability ceteris paribus (c.p.) leads to less tax evasion. Allingham and Sandmo (1972) find that higher penalty rates, ceteris paribus, rise the optimal income declared and, thus, reduce the theoretical extent of tax evasion. The remaining comparative static results require additional assumptions. For instance, Srinivasan (1973) considers simultaneously (i) a progressive tax scheme and (ii) an income-independent audit probability. Then, raising the income, ceteris paribus, increases the declared fraction of income understatement and, therefore, tax evasion. To put it differently, richer taxpayers evade more tax – in relative and absolute terms – if a progressive income tax tariff applies. Further, the author examines an increase in income given (i) constant marginal tax rates and (ii) increasing audit probabilities. Here, the opposite effect occurs; that is, a higher income, ceteris paribus, decreases the magnitude of tax evasion. Allingham and Sandmo (1972) consider an increase of income and simultaneously analyze (i) a reduction of absolute risk aversion and (ii) a constant penalty rate, which is equal or greater than one. In this case, a larger income, ceteris paribus, triggers a higher optimal income declared and, therefore, leads to less tax evasion. Next, in addition to optimal income declared, a fraction of income declared is studied. In this context, it is worth noting that fractions of taxpayer's true income (Allingham and Sandmo, 1972) and income understatement (Srinivasan, 1973) are counterparts and add up to unity. The group of authors finds variations of fractions declared to tax authorities depending on taxpayer's relative risk aversion. Allingham and Sandmo (1972) introduce an income and substitution effect to the tax evasion theory, which can be traced back to their modeling of tax and penalty rates. The authors observe negative substitution effects since rising tax rates enhance taxpayer's incentives to evade tax. The sign of the income effect is ambiguous and depends on taxpayer's absolute risk aversion. For instance, decreasing absolute risk aversion yields strictly positive income effects such that the model fails to provide a clear-cut hypothesis. In summary, ceteris paribus, lower extents of tax evasion are caused by separately increasing the two enforcement parameters (i) audit probability and (ii) penalty rate, whereas all other comparative statics results by Allingham and Sandmo (1972) or Srinivasan (1973) require further assumptions.

Fourth, the authors present various extensions of their theoretical frameworks. Allingham and Sandmo (1972) examine three additional features, which are (i) lapse of time effects (or back auditing), (ii) nonpecuniary factors and (iii) variable audit probabilities. Concerning the last feature, comparative statics support the notion that more audit efforts, ceteris paribus, reduce tax evasion if and only if the audit function is monotone decreasing and strictly concave with respect to income. Nonpecuniary factors are added to taxpayer's utility function, for example, to reflect shame and guilt of identified and punished tax evaders. Allingham and Sandmo (1972) show the impact of such a modeling on taxpayer's evading constraints (Eq. (1.5)), even though the signs are not clear. With respect to back auditing, the authors find tipping points when a representative taxpayer starts to declare almost everything honestly.³ Srinivasan (1973) studies two other extensions, which are (i) progressive versus proportional tax tariffs and (ii) optimization of audit probabilities. Considering various feasible tax tariffs, the author obtains that flat tax, ceteris paribus, yields less tax evasion than progressive tax schemes. With respect to an audit optimization procedure, he deduces a precondition that depends on marginal governmental expenditures due to the costs of raising audit probabilities. To sum up, Allingham and Sandmo (1972) and Srinivasan (1973) find that variable audit probabilities, lapse of time effects and changes of tax tariffs, for example, to implement flat tax, reduce tax evasion while the remaining extensions, for instance nonpecuniary factors, yield no clear-cut conclusions.

Finally, both tax evasion models are subject to notable criticism. One of the outstanding problems is that both theoretical frameworks in their standard version simply over-predict the amount of income tax evasion, which is estimated in reality. This is inconsistent with the real-world magnitudes of tax enforcement variables, which are obviously too low to guarantee deterrence levels that are theoretically necessary for taxpayers to become fully tax compliant. Therefore, the emerging crucial research question is the taxpayer's compliance mystery, why are they so tax compliant or intend to be totally compliant? To put this differently, the challenging issue is not, why tax avoidance, evasion, and the like exist but on the contrary it is the well-known question: “Why do people pay taxes?” (Alm et al., 1992b). Moreover, on the technical side, the Yitzhaki (1974) criticism deals with the problem of ambiguous income and substitution effects in the standard setting by Allingham and Sandmo (1972). Yet, Yitzhaki (1974) himself has suggested a solution; that is, the penalty rate has to depend on evaded tax rather than on nondeclared income. Under these circumstances the assumption of decreasing absolute risk aversion, with increasing income, yields pure income and no substitution effects so that higher tax rates, ceteris paribus, reduce the extent of tax evasion. Obviously, Srinivasan (1973) is not subject to the Yitzhaki (1974) critique because of penalty rates that are based on income understatement.

In addition to the critics of the components of the models, there are also a number of critics of these models based upon missing elements. These critics are not unique to these foundational tax evasion models and relate to issues of the heterogeneity of taxpayer behavior, potential taxpayer learning and adaptation over time, the potential impact of social networks, and the role of intermediaries such as tax preparers.

Despite the aforementioned critics, the standard theoretical model proposed by Allingham and Sandmo (1972) has become the standard theoretical model to analyze income tax evasion. The approach is still a fertile origin for rich work concerning tax evasion and related issues (e.g., for empirical observations see Kleven et al., 2011, for applications to the shadow economy see Buehn and Schneider, 2012; Slemrod and Weber, 2012). Since the early 1970s, considerable extensions have been added to correct, enlarge, and adjust (Allingham and Sandmo, 1972), for instance misperceptions of tax enforcement variables, psychological effects and social norms (e.g., see Myles and Naylor, 1996; Fortin et al., 2007, for a survey on psychological incentives of tax evasion see Kirchler, 2007). Yet, model extensions frequently generate such a complexity that clear-cut hypotheses are not available (e.g., see Alm, 2012, pp. 60–64). Of course, without any doubt, income tax evasion dynamics clearly influence tax revenues and public budgets. The above discussion outlined the canonical economic foundations for the analysis of tax paying behavior; next we will discuss the use of agent-based modeling in this endeavor.

1.4 Agent-Based Models

The rapid increase in computing power over the past several decades has led to a widespread usage of computers for conducting research via simulation. The social sciences in particular have turned to computer simulations as a technique to investigate complex real-world situations. Garson (2009, p. 267) identifies the main research branches of computational social simulation as: (i) ABMs, (ii) network models, (iii) spatial models, and (iv) systems dynamics models. The last mentioned consider digital-programmed systems of equations (or rules) that allow for illuminating complex socio-economic systems, for example, “The limits of economic growth” by Meadows et al. (1972). Spatial models simulate the interaction between a geographical (or physical) environment and, for instance, human behavior patterns. Network models cover a variety of topics; for example, from neural networks to queuing theory and its application to traffic problems (Gilbert and Troitzsch, 2005). ABMs, the focus of this book, consist of discrete autonomous agents that behave according to prescribed decision rules. Interaction of agents at the micro-level often leads to complex emergent phenomena at the macro-level.

Individual decisions on tax evasion are embedded in a highly complex environment of behavioral rules, social norms, and tax enforcement (Kirchler, 2007). Our focus on the use of ABMs is driven by their ability to explore the heterogeneous behaviors of large populations that can result from this complexity. This is in rich contrast to the standard neoclassical approach based on a single representative agent (see Alm, 2010; Bloomquist, 2011a). Furthermore, ABMs investigate the interaction of adaptive agents and allow for the use of tools from related branches; for example, systems dynamics models to describe the behavior patterns and the interaction rules of the agents and spatial and network models to describe an agent's physical environment and social neighborhood, respectively (Carley and Maxwell, 2006). Hence, agent-based modeling seems to be a promising tool for research on complex social systems such as tax evasion in societies of behaviorally heterogeneous agents (for overviews on agent-based simulations see Garson, 2009; Heath et al., 2009; Schinckus, 2013, for surveys on agent-based tax evasion models see Bloomquist, 2006; Hokamp, 2013; Pickhardt and Seibold, 2014; Bazart et al., 2016, the insights from tax evasion theory, income declaration experiments and field studies are surveyed by Alm, 2012, the behavioral dynamics of tax compliance are reviewed by Pickhardt and Prinz, 2014). In particular, Garson (2009, p. 271) employs tax evasion as an example to point out that “[…] simulation is a way to explore assumptions, not necessarily to find a “correct” solution or optimal set of parameters […].” The above discussion focused on the “why” of agent-based modeling, next we discuss how to report ABMs to aid in the creation of a cumulative science.

1.5 Standard Protocols to Describe Agent-Based Models

In this book we focus on model-based science, specifically the use of ABMs to explore more realistic, or higher resolution, representations of taxpayers and the tax payment system. Here, one uses the ABM to generate “sufficiency theorems” (Axtell, 2000a): for example, a population of agents acting under certain behavioral rules and specific conditions are sufficient to produce the observed dynamics and structures. In this work we stress the importance of clearly and thoroughly explaining the simulations used because we feel that this is a science. This being the case, we must ensure that the work can be understood, evaluated, and extended by others; and not seen as a “black box” (Lorscheid et al., 2012). In order to make the claim that we are engaged in science we must create “theories.” For our purposes, theories are statements about the world that are sufficiently specific as to be falsifiable, general enough to be comprehensive, and simple enough to be parsimonious (the ratio of predictions to assumptions should be large) (Harte, 2011). Here, the output of a run of the model serves as a prediction, it is a strict deduction (Epstein, 2006). Ideally, this prediction is sufficiently specific as to be falsifiable. One can then use collections of output (deductions) to inductively build up theories, here, of human behavior.

As with most scientific endeavors, our work should be cumulative and build upon a foundation of previous research. This requires that enough information be reported to allow for replication, and then extension, of previous work. To that end, one may say that all researchers should be required to post their code. Arguably, that could be even better than a well expressed formulation (narrative), and certainly more efficient from a cumulative perspective. However, that would mean that researchers may understand less of the foundation they are using and, more importantly, could perpetuate unexpressed biases in implementation choices and bugs that may go unnoticed. If prior simulation-based work is re-implemented, then these assumptions are more likely to be discovered and previous bugs are less likely to be perpetuated (which is not to imply that potentially new bugs will not be introduced).

A second reason to stress the importance, and use, of a standard protocol to document computational simulations is for validation and verification purposes. These two concepts become increasingly important as the use of the models and simulation move from academic thought experiments to decision support systems used by policy makers. Verification is the process of deciding if the model matches its specification. Validation is the process of deciding how well a model matches the “real-world” phenomena under study. It is through this process that one can develop and document an understanding of how the model relates to the real world and how much “faith” to place in its predictions (a general process typically referred to as accreditation). One process to use in this endeavor is that of Docking (Axtell et al., 1996) and categorizing the ABM's empirical relevance (Axtell, 2005). Docking refers to the process of comparing your model to a referent system (usually another model). There are three degrees of docking: Identity, where the two models produce numerically identical results; Distributional, where the models produce statistically indistinguishable results; and Relational, where the models produce qualitatively similar results that are statistically distinct. The empirical relevance of a model is a way to characterize how well the model represents both the micro-level (individuals) and macro-level (emergent structure) of the real world under study. Level 0 is micro-level qualitative correspondence; Level 1 is macro-level qualitative correspondence; Level 2 is macro-level quantitative correspondence, and finally, Level 3 is micro-level quantitative correspondence. The required level of empirical relevance is a function of how one plans to use the model. This process should be done with the model's intended purpose and audience in mind. For example, if one is creating an ABM simply to help think through a particular generating mechanism, then Level 0, Relational correspondence to the real world is likely to be sufficient. Here, the agents behave plausibly and, as a whole, the system changes in an appropriate manner when inputs are adjusted. However, if one is creating a model to be used by policy makers as they reform a taxation system then a higher standard should be used. Under these circumstances one would likely want to achieve at least Level 2, Empirical Relevance and Distributional Equivalence. Meaning, if income in the real world is Zipf distributed, the income distribution within the simulation is also Zipf distributed and is statistically indistinguishable form that of the real world.

1.6 Literature Review of Agent-Based Tax Evasion Models

In this section, we trace the evolution of agent-based tax compliance modeling and briefly outline recent advances. The agent-based frameworks highlight the need to model tax noncompliance decisions not in isolation, but rather embedded within a complex environment. The characteristics of the different methodologies used are summarized in Tables 1.2–1.4 presenting two highlights (or main areas) per agent-based tax noncompliance methodology and categorizing them with respect to (i) lead authors and research groups, (ii) software, (iii) domain, (iv) population size, (v) public goods, (vi) governmental tasks, (vii) back auditing, (viii) replication and docking studies, (ix) calibration, and (x) model highlights. The literature review is based on six surveys; (i) Bloomquist (2006) on the three early agent-based tax noncompliance frameworks by Mittone and Patelli (2000), Davis et al. (2003), and Bloomquist (2004a,b, 2008), (ii) Alm (2012) on tax evasion theories, income declaration experiments, and field studies, (iii) Hokamp (2013) on agent-based tax evasion and noncompliance models (iv) Pickhardt and Prinz (2014) on the behavioral dynamics of tax compliance, (v) Oates (2015) on tax evasion literature, and (vi) Bazart et al. (2016) on the calibration of agent-based tax evasion models.

Inspection of Tables 1.2–1.4 permits us to identify more than 30 agent-based settings of tax noncompliance, although Kim (2003), Meacci et al. (2012), Bertotti and Modanese (2014a,b, 2016a,b), and Nicolaides (2014) might be considered as borderline cases. The sequential arrangement of methodologies is alphabetic by the lead author of the very first contribution with respect to each research group. Thus, the first letter of the lead author ranges from A to C, in Table 1.2, from D to MA, in Table 1.3, and from MB to W, in Table 1.4. The research groups are not strictly disjoint, for instance L. Antunes, K. M. Bloomquist, S. Hokamp, M. Koehler, L. Mittone, M. Pickhardt, and F. W. S. Lima provide more than one agent-based tax noncompliance methodology. Moreover, seven research groups provide an abbreviation of their ABM: (i) Tax Compliance Simulator (TCS, Bloomquist, 2004a,b, 2008), (ii) Networked Agent-based Compliance Model (NASCM, Korobow et al., 2007), (iii) Agent-based Tax Evasion Simulator (TAXSIM, Szabó et al., 2009, 2010; Gulyás et al., 2015), (iv) Small Business Tax Compliance Simulator (SBTCS, Bloomquist, 2011a), (v) Individual Reporting Compliance Model (IRCM Bloomquist, 2011b, 2013; Bloomquist and Koehler, 2015), (vi) Model C (Méder et al., 2012) and (vii) SIMULFIS (Llacer et al., 2013; Noguera et al., 2014).

Additional columns describe the software utilized, the domain classifications as an economics or econophysics setting⁴ and the magnitude of population considered. The software utilized ranges from open source (for instance, NetLogo, RePast HPC) to restricted and commercial software (e.g., Mathematica, MATLAB). With respect to the classification in a domain, the majority of frameworks belongs to economics (28 out of 32), but econophysics seems to gain more and more attractiveness since the seminal paper by Zaklan et al. (2009). S. Hokamp and M. Pickhardt contribute to both, the economics and econophysics branch (Hokamp and Pickhardt, 2010; Seibold and Pickhardt, 2013; Hokamp, 2014; Hokamp and Seibold, 2014b; Pickhardt and Seibold, 2014; Bazart et al., 2016). The population size ranges from 10 taxpayers (see Vale, 2015) to agents (see Cline et al., 2014), while econophysics ABMs deal with up to taxpayers (e.g., see Zaklan et al., 2009). Notably, Cline et al. (2014) were the first to attempt a massive-scale agent-based tax evasion model, without roots in econophysics, to investigate a society of taxpayers.

Furthermore, Tables 1.2–1.4 allow for jointly discussing and visualizing public goods provision, governmental tasks, back auditing, replication and docking issues, calibration and two highlights for each model. We provide a detailed overview of these issues in the next subsections.

Research group	Software	Domain		Population size	Public goods	Governmental tasks	Back auditing	Replication/docking study	Calibration	Highlights
Andrei et al. (2014)	NetLogo	Economics		441	–	–	–	Korobow et al. (2007)	–	Docking study
Chapter 8								Hokamp and Pickhardt (2010)		Network structures
Antunes et al. (2006, 2007a,b)	NetLogo	Economics		500		–		–	–	Back auditing
Balsa et al. (2006)										Social interactions
Arsian and İcan (2013a,b)	NetLogo	Economics		10,000	–	–	–	Bloomquist (2011a)	Turkish Revenue Administration	Audit perception
										Social networks
Bertotti and Modanese (2014a,b, 2016a,b)	–	Economics		25a	–		–	–	–	Income classes
										Trade
Bloomquist (2004a,b, 2008)	NetLogo	Economics	(i)	300	–	–	–	–	–	Life span
			(ii)							Social networks
Bloomquist (2011a)	NetLogo	Economics			–	–	–	–	Experiments / Internal Revenue Service	Bankruptcy
										Calibration
Bloomquist (2011b, 2013)	RePast	Economics			–	–	–	–	Internal Revenue Service	Artificial county
Bloomquist and Koehler (2015) Chapter 7										Third-party reporting
Carley and Maxwell (2006)	Construct	Economics		–	–	–	–	–	–	Advertising campaign
										Synthetic city
Cline et al. (2014)	RePast HPC	Economics		12,000,000	–	–	–	Bloomquist (2011b)	U.S. synthesized population dataset	Massive-scale
Chapter 8								Andrei et al. (2014)		Social networks
Crokidakis (2014)	–	Econophysics		10,000	–	–	–	Zaklan et al. (2009)	–	Opinion exchange dynamics
										Three states of tax declaration

“Research Group” allows for assigning the agent-based tax evasion frameworks to teams of scholars in alphabetic order that refers to the leading author regarding the first contribution. “Software” shows computational tools. “–” denotes no information. “Domain” classifies the settings with respect to the economics or the econophysics modeling branch. “Population Size” lists the number of agents for scenarios in order of appearance, denoted as (i), (ii), and (iii), ^a The income classes in Bertotti and Modanese (2014a,b, 2016a,b). “X” represents an agent-based setting of tax noncompliance that incorporates “Public Goods,” “Governmental Tasks,” and “Back Auditing,” respectively. “Replication/Docking Study” permits to figure out the replicated frameworks. “Calibration” presents the data source used, “Highlights” provides two key features per setting.

Research group	Software	Domain		Population size	Public goods	Governmental tasks	Back auditing	Replication/docking study	Calibration	Highlights
Davis et al. (2003)	Mathematica	Economics		500	–	–	–	–	–	Compliance periods
Garrido and Mittone (2013)	–	Economics		180	–	×	–	–	Experiments	Social norms
Chapter 3										Audit frequency
										Optimal audit programs
Hashimzade et al. (2014–2016)	MATLAB	Economics	(i)		–		–	–	–	Audit strategy
Hashimzade and Myles (2017)			(ii)							Occupational choice
Chapter 4
Hokamp (2014) Chapter 9	RePast	Economics						Hokamp and Pickhardt (2010)	–	Pareto-optimality
										Social norm updating
Hokamp and Pickhardt (2010)	MATLAB	Economics			–			–	–	Back auditing
Chapter 9										Political cycle
Kim (2003)	–	Economics		–	–		–	–	–	Audit policy
										Social coordination
Korobow et al. (2007)	–	Economics			–	–	–	–	–	Heat maps
										Social neighborhoods
Lima (2010, 2012a,b)	–	Econophysics	(i)	1,000,000	–		–	Zaklan et al. (2009)	–	Majority voting
			(ii)	400						Replication study
			(iii)	4,000
Lima and Zaklan (2008)	Fortran	Econophysics	(i)	400	–		–	–	–	Ising-model
Zaklan et al. (2008, 2009)			(ii)	1,000,000						Network structures
Llacer et al. (2013)	NetLogo	Economics		–	–		–	–	Spanish empirical data	Learning mechanisms
Noguera et al. (2014)										Social benefits
Chapter 5
Magessi and Antunes (2013a,b, 2015)	NetLogo	Economics	(i)	20	–	–	–	–	Portuguese survey data	Greed
			(ii)	1,000						Risk perception
Manhire (2015)	NetLogo	Economics	(i)	19a;b	–		–	–	–	Audit effects
			(ii)	0a–125a;b						Tax compliance puzzle

^a The number of tax examiners Manhire (2015).

^b The taxpayers in Manhire. For a brief description of the syntax see Table 1.2.

Research group	Software	Domain		Population size	Public goods	Governmental tasks	Back auditing	Replication/docking study	Calibration	Highlights
Meacci et al. (2012)		Economics		1,600	–		–	–	–	Cellular automata
										Cross-border policy
Méder et al. (2012)	NetLogo	Economics		1,000			–	–	–	Laffer-curves
										No enforcement
Mittone and Patelli (2000) Chapter 3	SWARM	Economics		300		–	–	–	–	Public goods
										Strategic auditing
Nicolaides (2014)	–	Economics		–			–	–	–	Institutional quality
										Social norms
Nordblom and Z̆amac (2012)	Java	Economics		10,000	–	–	–	–	Swedisch Tax Agency Survey	Black market
										Life cycle
Pellizzari and Rizzi (2014)	–	Economics		1,000			–	–	–	Individual preferences
										Slippery-slope framework
Seibold and Pickhardt (2013)	Fortran	Econophysics	(i)	1,000,000				Zaklan et al. (2009)	Experiments	Magnetic fields
Hokamp and Seibold (2014b)			(ii)	150,000				Hokamp and Pickhardt (2010)		Temperature
Pickhardt and Seibold (2014)
Bazart et al. (2016)
Chapter 11
Szabó et al. (2009, 2010)	RePast	Economics	(i)	200a; 40b			–	–	–	(Closed) Economy
Gulyás et al. (2015)			(ii)	500a; 50b						Job market
Chapter 6
Vale (2015)	–	Economics	(i)	10	–	–		–	–	Social networks
			(ii)	100						Varying evasion probability
Warner et al. (2015)	–	Economics		–	–	–	–	–	–	Genetic algorithms
Rosen et al. (2015)										Tax evasion schemes
Hemberg et al. (2016)
Chapter 10

In Szabó et al. (2009, 2010) ^adenotes the number of workers and ^bdenotes the number of employers.

1.7 Outlook: The Structure and Presentation of the Book

Our book is structured as follows. Part I includes this introductory chapter that provides a conceptual background, a review of agent-based modeling, and the literature on tax evasion. It also discusses “dark” economic behavior in general and the methodological link between experiments and agent-based modeling. Part II presents various applications of agent-based modeling to tax evasion, constructed for or calibrated to various countries (the United Kingdom, the United States, Spain, Hungary, and Germany). This is completed by two chapters extending the horizon of computational models of tax evasion. One applies genetic algorithms to co-evolve tax audit strategies with clandestine behavior, in order to “breed” possible novel forms of tax evasion. The other brings an “econophysics” approach to the problem by developing a variant of a classic model of ferromagnetism adapted to tax evasion.

References

1. Allingham, M.G. and Sandmo, A. (1972) Income tax evasion: a theoretical analysis. Journal of Public Economics, 1, 323–338.
2. Alm, J. (2010) Testing behavioral public economic theories in the laboratory. National Tax Journal, 63 (4), 635–658.
3. Alm, J. (2012) Measuring, explaining, and controlling tax evasion: lessons from theory, experiments, and field studies. International Tax and Public Finance, 19 (1), 54–77.
4. Alm, J., Jackson, B., and McKee, M. (1992a) Institutional uncertainty and taxpayer compliance. The American Economic Review, 82 (4), 1018–1026.
5. Alm, J., McClelland, G.H., and Schulze, W.D. (1992b) Why do people pay taxes? Journal of Public Economics, 48, 21–38.
6. Alm, J., Jackson, B.R., and McKee, M. (2009) Getting the word out: enforcement information dissemination and compliance behavior. Journal of Public Economics, 93, 392–402.
7. Andreoni, J., Erard, B., and Feinstein, J. (1998) Tax compliance. Journal of Economic Literature, 36 (2), 818–860.
8. Andrei, A.I., Comer, K., and Koehler, M. (2014) An agent-based model of network effects on tax compliance. Journal of Economic Psychology, 40, 119–133.
9. Antunes, L., Balsa, J., and Coelho, H. (2007a) Tax compliance through MABS: the case of indirect taxes, in Progress in Artificial Intelligence, EPIA 2007, LNAI, vol. 4874, Springer-Verlag, Berlin, Heidelberg, pp. 605–617.
10. Antunes, L., Balsa, J., Respício, A., and Coelho, H. (2007b) Tactical exploration of tax compliance decisions in multi-agent based simulation, in Multi-Agent-Based Simulation VII, International Workshop MABS 2006, LNAI, vol. 4442, Springer-Verlag, Berlin, Heidelberg, pp. 80–95.
11. Antunes, L., Balsa, J., Urbano, P., Moniz, L., and Roseta-Palma, C. (2006) Tax compliance in a simulated heterogeneous multi-agent society, in Multi-AGENT-BASED SIMULATION VI, International Workshop MABS 2005, LNAI, vol. 3891, Springer-Verlag, Berlin, Heidelberg, pp. 147–161.
12. Arsian, O. and İcan, Ö. (2013a) An agent-based analysis of tax compliance for Turkey. Andolu University Journal of Social Sciences, 13 (2), 143–152.
13. Arsian, O. and İcan, Ö. (2013b) The effects of neighborhood on tax compliance rates: evidence from an agent-based model. C.Ü. Sosyal Bilimler Enstitüsü Dergisi, 22 (1), 337–350.
14. Axtell, R. (2000a) Why agents? On the varied motivations for agent computing in the social sciences. Brookings Institution Center on Social and Economic Dynamics working paper.
15. Axtell, R. (2000b) Effects of Interaction Topology and Activation Regime in Several Multi-Agent Systems, Springer-Verlag, Berlin, Heidelberg.
16. Axtell, R. (2005) Three distinct kinds of empirically-relevant agent-based models. Brookings Institution Center on Social and Economic Dynamics working paper.
17. Axtell, R., Axelrod, R., Epstein, J.M., and Cohen, M.D. (1996) Aligning simulation models: a case study and results. Computational & Mathematical Organization Theory, 1 (2), 123–141.
18. Balsa, J., Antunes, L., Respício, A., and Coelho, H. (2006) Autonomous Inspectors in Tax Compliance Simulation. Proceedings of the 18th European Meeting on Cybernetics and Systems Research, April 2006, Vienna, Austria.
19. Bazart, C. and Bonein, A. (2014) Reciprocal relationships in tax compliance decisions. Journal of Economic Psychology, 40, 83–102.
20. Bazart, C., Bonein, A., Hokamp, S., and Seibold, G. (2016) Behavioural economics and tax evasion – calibrating an agent-based econophysics model with experimental tax compliance data. Journal of Tax Administration, 2 (1), 126–144.
21. Bazart, C. and Pickhardt, M. (2011) Fighting income tax evasion with positive rewards. Public Finance Review, 39 (1), 124–149.
22. Becker, G.S. (1968) Crime and punishment: an economic approach. The Journal of Political Economy, 76 (2), 169–217.
23. Becker, G.S. (1993) Nobel lecture: the economic way of looking at behavior. The Journal of Political Economy, 101 (3), 385–409.
24. Bertotti, M.L. and Modanese, G. (2014a) Micro to macro models for income distribution in the absence and in presence of tax evasion. Applied Mathematics and Computation, 224, 836–846.
25. Bertotti, M.L. and Modanese, G. (2014b) Mathematical models for socio-economic problems, in Mathematical Models and Methods for Planet Earth, Springer, Switzerland, pp. 124–134.
26. Bertotti, M.L. and Modanese, G. (2016a) Microscope Models for the Study of Taxpayer Audit Effects, arXiv 1602.08467v1 [q-fin.GN] 18 February 2016.
27. Bertotti, M.L. and Modanese, G. (2016b) Mathematical models describing the effects of different tax evasion behaviors. Journal of Economic Interaction and Coordination, 1–13.
28. Bloomquist, K.M. (2004a) Modeling Taxpayers' Response to Compliance Improvement Alternatives. Paper presented at the Annual Conference of the North American Association for Computational Social and Organizational Sciences, Pittsburgh, PA.
29. Bloomquist, K.M. (2004b) Multi-agent Based Simulation of the Deterrent Effects of Taxpayer Audits. Paper presented at the 97th Annual Conference of the National Tax Association, Minneapolis, MN.
30. Bloomquist, K.M. (2006) A comparison of agent-based models of income tax evasion. Social Science Computer Review, 24 (4), 411–425.
31. Bloomquist, K.M. (2008) Tax compliance simulation: a multi-agent based approach, in Social Simulation: Technologies, Advances and New Discoveries, IGI Global, pp. 13–25.
32. Bloomquist, K.M. (2011a) Tax compliance as an evolutionary coordination game: an agent-based approach. Public Finance Review, 39 (1), 25–49.
33. Bloomquist, K.M. (2011b) Multi-Agent Simulation of Taxpayer Reporting Compliance. Invited Paper presented at the International Conference on Taxation Analysis and Research, December 2011, London, UK.
34. Bloomquist, K.M. (2012) Agent-based simulation of tax reporting compliance. PhD thesis. George Mason University.
35. Bloomquist, K.M. (2013) Incorporating Indirect Effects in Audit Case Selection: An Agent-Based Approach, The IRS Research Bulletin, Publication 1500, pp. 103–116.
36. Bloomquist, K.M. and Koehler, M. (2015) A large-scale agent-based model of taxpayer reporting compliance. Journal of Artificial Societies and Social Simulation, 18 (2). doi: 10.18564/jasss.2621.
37. Blume, L.E. (1993) Statistical mechanics of strategic interaction. Games and Economic Behaviour, 5, 387–424.
38. Buehn, A. and Schneider, F. (2012) Shadow economies around the world: novel insights, accepted knowledge, and new estimates. International Tax and Public Finance, 19 (1), 139–171.
39. Carley, K.M. and Maxwell, D.T. (2006) Understanding Taxpayer Behavior and Assessing Potential IRS Interventions Using Multiagent Dynamic-network Simulation. Recent Research on Tax Administration and Compliance: Selected Papers Given at the 2006 IRS Research Conference, Statistics of Income Division, Internal Revenue Service, Department of the Treasury, Washington, DC, pp. 93–106.
40. Cline, J., Bloomquist, K.M., Gentile, J.E., Koehler, M., and Marques, U. (2014) From Thought to Action: Creating Tax Compliance Models at National Scales. Paper presented at the 11th International Conference on Tax Administration, April 2014, Sydney, Australia.
41. Cowell, F.A. (1992) Tax evasion and inequity. Journal of Economic Psychology, 13, 521–543.
42. Cowell, F. and Gordon, J.P.F. (1988) Unwillingness to pay - tax evasion and public goods provision. Journal of Public Economics, 36, 305–321.
43. Crokidakis, N. (2014) A three-state kinetic agent-based model to analyze tax evasion dynamics. Physica A, 414, 321–328.
44. Davis, J., Hecht, G., and Perkins, J.D. (2003) Social behaviors, enforcement and tax compliance dynamics. The Accounting Review, 78, 39–69.
45. Dibble, C. (2006) Computational laboratories for spatial agent-based models. Handbook of Computational Economics, 2, 1511–1548.
46. Epstein, J.M. (2006) Generative Social Science: Studies in Agent-Based Computational Modeling, Princeton University Press.
47. Fortin, B., Lacroix, G., and Villeval, M.C. (2007) Tax evasion and social interactions. Journal of Public Economics, 91, 2089–2112.
48. Garay, B.M., Simonovits, A., and Tóth, I.J. (2012) Local interaction in tax evasion. Economics Letters, 115, 412–415.
49. Garrido, N. and Mittone, L. (2013) An agent based model for studying optimal tax collection policy using experimental data: the cases of Chile and Italy. Journal of Socio-Economics, 42, 24–30.
50. Garson, G.D. (2009) Computerized simulation in the social sciences - a survey and evaluation. Simulation and Gaming, 20 (2), 267–279.
51. Gilbert, N. and Troitzsch, K.G. (2005) Simulation for the Social Scientist, Open University Press.
52. Government Accountability Office (2012) TAX GAP. Sources of Non-Compliance and Strategies to Reduce It. GAO-12-651T, http://www.gao.gov/assets/600/590215.pdf (accessed 6 May 2016).
53. Grimm, V. et al. (2006) A standard protocol for describing individual-based and agent-based models. Ecological Modelling, 198 (1), 115–126.
54. Grimm, V. et al. (2010) The ODD protocol: a review and first update. Ecological Modelling, 221 (23), 2760–2768.
55. Grimm, V. and Schmolke, A. (2011) How to Read and Write TRACE Documentations, http://cream-itn.eu/creamwp/wp-content/uploads/Trace-Guidance-11-03-04.pdf (accessed 18 December 2016).
56. Gulyás, L., Máhr, T., and Tóth, I.J. (2015) Factors to Curb Tax Evasion: Evidence from the TAXSIM Agent-based Simulation Model. KTI/IE Discussion Papers, MP-DP – 2015/21, April 2015, Budapest, Hungary.
57. Harte, J. (2011) Maximum Entropy and Ecology: A Theory of Abundance, Distribution, and Energetics, Oxford University Press.
58. Hashimzade, N. and Myles, G.D. (2017) Risk-based audits in a behavioural model. Public Finance Review, 45 (1), 130–145.
59. Hashimzade, N., Myles, G.D., Page, T., and Rablen, M.D. (2014) Social networks and occupational choice: the endogenous formation of attitudes and beliefs about tax compliance. Journal of Economic Psychology, 40, 134–146.
60. Hashimzade, N., Myles, G.D., Page, T., and Rablen, M.D. (2015) The use of agent-based modelling to investigate tax compliance. Economics of Governance, 16, 143–164.
61. Hashimzade, N., Myles, G.D., and Rablen, M.D. (2016) Predictive analytics and the targeting of audits. Journal of Economic Behavior & Organization, 124, 130–145.
62. Heath, B., Hill, R., and Ciarallo, F. (2009) A survey of agent-based modelling practices (January 1998 to July 2008). Journal of Artificial Societies and Social Simulation, 12, (4), 9.
63. Hemberg, E., Rosen, J., Warner, G., Wijesinghe, S., and O'Reilly, U.-M. (2016) Detecting tax evasion: co-evolutionary approach. Artificial Intelligence and Law, 24 (2), 149–182.
64. Hokamp, S. (2013) Income tax evasion and public goods provision – theoretical aspects and agent-based simulations. PhD thesis. Brandenburg University of Technology Cottbus.
65. Hokamp, S. (2014) Dynamics of tax evasion with back auditing, social norm updating, and public goods provision – an agent-based simulation. Journal of Economic Psychology, 40, 187–199.
66. Hokamp, S. and Pickhardt, M. (2010) Income tax evasion in a society of heterogeneous agents – evidence from an agent-based model. International Economic Journal, 24 (4), 541–553.
67. Hokamp, S. and Seibold, G. (2014a) How much rationality tolerates the shadow economy? – An agent-based econophysics approach, in Advances in Social Simulation, ESSA 2013, Advances in Intelligent Systems and Computing, vol. 229, Springer-Verlag, Berlin, Heidelberg, pp. 119–128.
68. Hokamp, S. and Seibold, G. (2014b) Tax compliance and public goods provision – an agent-based econophysics approach. Central European Journal of Economic Modelling and Econometrics, 6 (4), 217–236.
69. Internal Revenue Service (2007) Reducing the Federal Tax Gap: A Report on Improving Voluntary Compliance, http://www.irs.gov./pub/irs-news/tax_gap_report_final_080207_linked.pdf (accessed 12 April 2012).
70. Internal Revenue Service (2016a) IRS Tax Gap Estimates for Tax Years 2008–2010, https://www.irs.gov/PUP/newsroom/tax gap estimates for 2008 through 2010.pdf (accessed 23 November 2016).
71. Internal Revenue Service (2016b) IRS Internal Revenue Manual, Part 25.1.1, https://www.irs.gov/irm/part25/irm_25-001-001.html#d0e119 (accessed 6 May 2016).
72. Ising, E. (1925) Beitrag zur Theorie des Ferromagnetismus. Zeitschrift für Physik, 31 (1), 253–258.
73. James, S. and Edwards, A. (2010) An Annotated Bibliography of Tax Compliance and Tax Compliance Costs, http://mpra.ub.uni-muenchen.de/26106/ (accessed 27 April 2012).
74. Kim, Y. (2003) Income distribution and equilibrium multiplicity in a stigma-based model of tax evasion. Journal of Public Economics, 87 (7–8), 1591–1616.
75. Kirchler, E. (2007) The Economic Psychology of Tax Behavior, Cambridge University Press, Cambridge.
76. Kleven, H.J., Knudsen, M.B., Kreiner, C.T., Perdersen, S., and Saez, E. (2011) Unwilling or unable to cheat? Evidence from a tax audit experiment in Denmark. Econometrica, 79 (3), 651–692.
77. Korobow, A., Johnson, C., and Axtell, R. (2007) An agent-based model of tax compliance with social networks. National Tax Journal, 60 (3), 589–610.
78. Krauskopf, T. and Prinz, A. (2011) Methods to reanalyze tax compliance experiments: Monte-Carlo simulations and decision time analysis. Public Finance Review, 39 (1), 168–188.
79. Lima, F.W.S. (2010) Analysing and controlling the tax evasion dynamics via majority-vote model. Journal of Physics: Conference Series, 246, 1–12.
80. Lima, F.W.S. (2012a) Tax evasion dynamics and Zaklan model on opinion-dependent network. International Journal of Modern Physics C: Computational Physics and Physical Computation, 23 (6). doi: 10.1142/s0129183112500477.
81. Lima, F.W.S. (2012b) Tax evasion and nonequilibrium model on apollonian networks. International Journal of Modern Physics C: Computational Physics and Physical Computation, 23 (11). doi: 10.1142/s0129183112500799.
82. Lima, F.W.S. and Zaklan, G. (2008) A multi-agent-based approach to tax morale. International Journal of Modern Physics C: Computational Physics and Physical Computation, 19 (12), 1797–1808.
83. Llacer, T., Miguel, F.J., Noguera, J.A., and Tapia, E. (2013) An agent-based model of tax compliance: an application to the Spanish case. Advances in Complex Systems, 16. doi: 10.1142/s0219525913500070.
84. Lorscheid, I., Heine, B.-O., and Meyer, M. (2012) Opening the “black box” of simulations: increased transparency and effective communication through the systematic design of experiments. Computational and Mathematical Organization Theory, 18, 22–62.
85. Magessi, N.T. and Antunes, L. (2013a) Modelling agent's risk perception, in Distributed Computing and Artificial Intelligence, DCAI 2013, Advances in Intelligent Systems and Computing, vol. 217, Springer-Verlag, Cham, Heidelberg, New York, Dordrecht, London, pp. 275–282.
86. Magessi, N.T. and Antunes, L. (2013b) Agent's Fear Monitors the Spread of Greed in a Social Network. Paper presented at the 11th European Workshop on Multi-Agent Systems, December 2013, Toulouse, France.
87. Magessi, N.T. and Antunes, L. (2015) Risk perception and risk attitude on a tax evasion context. Central European Journal of Economic Modelling and Econometrics, 7 (3), 127–149.
88. Manhire, J.T. (2015) There is no spoon: reconsidering the tax compliance puzzle. Florida Tax Review, 17 (8), 623–668.
89. Meacci, L., Nuño, J.C., and Primicerio, M. (2012) Fighting tax evasion: a cellular automata approach. Advances in Mathematical Sciences and Applications, 22 (2), 597–610.
90. Meadows, D.H., Meadows, D.L., Randers, J., and Behrens, W.W. III (1972) The Limits of Economic Growth, Universe Books.
91. Méder, Z.Z., Simonovits, A., and Vincze, J. (2012) Tax morale and tax evasion: social preferences and bounded rationality. Economic Analysis and Policy, 42 (2), 171–188.
92. Miguel, F.J., Noguera, J.A., Llacer, T., and Tapia, E. (2012) Exploring Tax Compliance: An Agent-Based Simulation. Paper presented at the 26th European Conference on Modelling and Simulation, May/June 2012, Koblenz, Germany.
93. Mittone, L. and Patelli, P. (2000) Imitative behavior in tax evasion, in Economic Simulations in Swarm: Agent-based Modelling and Object Oriented Programming, Kluwer Academic, Dordrecht, Boston, MA, London, pp. 133–158.
94. Müller, B. et al. (2013) Describing human decisions in agent-based models-ODD+ D, an extension of the ODD protocol. Environmental Modelling & Software, 48, 37–48.
95. Myles, G.D. and Naylor, R.A. (1996) A model of tax evasion with group conformity and social custom. European Journal of Political Economy, 12, 49–66.
96. Nicolaides, P. (2014) Tax compliance social norms and institutional quality: an evolutionary theory of public good provision. Taxation Papers, working paper 46 – 2014, Luxembourg.
97. Noguera, J.A., Llacer, T., Miguel, F.J., and Tapia, E. (2014) Tax compliance, rational choice, and social influence: an agent-based model. Revue Française de Sociologie, 55 (4), 765–804.
98. Nordblom, K. and Z̆amac, J. (2012) Endogenous norm formation over the life cycle – the case of tax morale. Economic Analysis and Policy, 42 (2), 153–170.
99. Oates, L. (2015) Review of recent literature. Journal of Tax Administration, 1 (1), 141–150.
100. Pellizzari, P. and Rizzi, D. (2014) Citizenship and power in an agent-based model of tax compliance with public expenditure. Journal of Economic Psychology, 40, 35–48.
101. Pickhardt, M. and Prinz, A. (2014) Behavioral dynamics of tax evasion – a survey. Journal of Economic Psychology, 40, 1–19.
102. Pickhardt, M. and Seibold, G. (2014) Income tax evasion dynamics: evidence from an agent-based econophysics model. Journal of Economic Psychology, 40, 147–160.
103. Rosen, J., Hemberg, E., Warner, G., Wijesinghe, S., and O'Reilly, U.-M. (2015) Computer Aided Tax Evasion Policy Analysis: Directed Search using Autonomous Agents. Proceedings of the 14th International Conference on Autonomous Agents and Multi-agent Systems (AAMAS 2015) (eds R.H. Bordini, E. Elkind, G. Weiss, and P. Yolum), May 4–8, 2015, Istanbul, Turkey.
104. Sandmo, A. (2012) An evasive topic: theorizing about the hidden economy. International Tax and Public Finance, 19 (1), 5–24.
105. Schelling, T.C. (1969) Models of segregation. American Economic Review, 59 (2), 488–493.
106. Schelling, T.C. (1971) Dynamic models of segregation. Journal of Mathematical Sociology, 1, 143–186.
107. Schinckus, C. (2013) Between complexity of modelling and modelling of complexity: an essay on econophysics. Physica A, 392 (13), 3654–3665.
108. Seibold, G. and Pickhardt, M. (2013) Lapse of time effects on tax evasion in an agent-based econophysics model, 2013. Physica A, 392 (9), 2079–2087.
109. Slemrod, J. (2007) Cheating ourselves: the economics of tax evasion. Journal of Economic Perspectives, 21 (1), 25–48.
110. Slemrod, J. and Weber, C. (2012) Evidence of the invisible: toward a credibility revolution in the empirical analysis of tax evasion and the informal economy. International Tax and Public Finance, 19 (1), 25–33.
111. Slemrod, J. and Yitzhaki, S. (2002) Tax avoidance, evasion and administration, in Handbook of Public Economics, North-Holland, Amsterdam, pp. 1425–1470.
112. Srinivasan, T.N. (1973) Tax evasion: a model. Journal of Public Economics, 2, 339–346.
113. Szabó, A., Gulyás, L., and Tóth, I.J. (2008) TAXSIM Agent Based Tax Evasion Simulator. Paper presented at the 5th Conference of the European Social Simulation Association, University of Brescia, Italy.
114. Szabó, A., Gulyás, L., and Tóth, I.J. (2009) Sensitivity analysis of a tax evasion model applying automated design of experiments, in Progress in Artificial Intelligence, 14th Portuguese Conference on Artificial Intelligence, EPIA 2009, Aveiro, Portugal, LNAI, vol. 5816, Springer-Verlag, Berlin, Heidelberg, pp. 572–583.
115. Szabó, A., Gulyás, L., and Tóth, I.J. (2010) Simulating tax evasion with utilitarian agents and social feedback. International Journal of Agent Technologies and Systems, 2 (1), 16–30.
116. Tesfatsion, L. (2006) Agent-based computational economics: a constructive approach to economic theory. Handbook of Computational Economics, 2, 831–880.
117. Torgler, B. (2002) Speaking to theorists and searching for facts: tax morale and tax compliance in experiments. Journal of Economic Surveys, 16, 657–683.
118. Vale, R. (2015) A model for tax evasion with some realistic properties. Working Paper available at Social Science Research Network.
119. Warner, G., Wijesinghe, S., Marques, U., Badar, O., Rosen, J., Hemberg, E., and O'Reilly, U.-M. (2015) Modeling tax evasion with genetic algorithms. Economics of Governance, 16, 165–178.
120. Wintrobe, R. and Gërxhani, K. (2004) Tax Evasion and Trust: A Comparative Analysis. Proceedings of the Annual Meeting of the European Public Choice Society, April 2004, Berlin, Germany.
121. Wolf, S. et al. (2013) Describing economic agent-based models-Dahlem ABM documentation guidelines. Complexity Economics, 2 (1), 63–74.
122. Yitzhaki, S. (1974) A note on income tax evasion: a theoretical analysis. Journal of Public Economics, 3, 201–202.
123. Zaklan, G., Lima, F.W.S., and Westerhoff, F. (2008) Controlling tax evasion fluctuations. Physica A: Statistical Mechanics and its Applications, 387 (23), 5857–5861.
124. Zaklan, G., Westerhoff, F., and Stauffer, D. (2009) Analysing tax evasion dynamics via the ising model. Journal of Economic Interaction and Coordination, 4, 1–14.