The Extortion Relationship : A Computational Analysis

Systematic extortion involves a long term parasitic relationship between the criminal and the victim. Game theory analysis has provided insight into the choices of individual hypothetical criminal and victim pairs. In thispaperwepresent anagent-basedmodel soas toextend theanalysis to the relationshipbetweenextorters and other potential victims. The model is developed in two stages, the first to be closest to game theory, the second one making the decision informed by the social environment of the victim. The agent-based model shows the importance of social aspects for the functioning of extortion rackets.


Introduction
. Extortion is the demand for money using the threat of violence.An extortion racket is the continuous, regular and systematic extortion of several victims by a criminal or (more usually) a criminal organisation.Extortion is di erent from other property crime such as burglary or fraud because of the long term, explicit and exploitative relationship between perpetrator and victim.It is also di erent from blackmail because extortion is o en endemic in a community or even society.
. There are some well-known examples of protection or extortion rackets.Probably the best known is the Italian Mafia, both in Italy (in particular the South and Sicily) and in migration countries such as the US and Germany (Gambetta ).In the estimated turnover of the Italian Mafia was thought to be around £ bn, which, at % of GDP, makes it Italy's biggest business .By definition, extortion racketeering is an essential feature of a Mafia Type Organisation (MTO), distinguishing MTOs from other organised crime groups (La Spina ).Other MTOs include the Russian Mafia (Smith and Varese ), motorcycle gangs such as the Hell's Angels and Bandidos, the Yakuza and a variety of gangs and drug cartels in Central and South America (Anzola and Elsenbroich ( )).
. One of the most prevalent scientific approaches to extortion rackets is a formalisation of the interdependent choices of extorters and entrepreneurs in game theory (such as Gambetta ; Konrad and Skaperdas ; Smith and Varese ).This formalisation adopts the rational choice paradigm underlying much of criminology (Becker ).But whereas usually the focus is on the decision of the criminal to commit a crime given a probability of punishment if caught, here the focus is the victim's decision to pay given the probability of being punished by an extorter.This punishment probability is influenced by exogenous factors such as the presence of police (so that Mafiosi are deterred from punishing) and, in some cases, the presence of fakers.Fakers are agents posing as Mafiosi and demanding payment but who will not punish resistors, due to fear of detection by police and real Mafiosi.We discuss these approaches in more detail in Section .

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Inspired by this approach we develop an agent-based model (ABM) of extortion racketeering to understand the dynamic interdependencies between punishment (for both deterrence and reputation) and levels of acquiescence in a society.The agent behaviour in our model also uses the rational paradigm.However, we take advantage of the dynamic nature of ABMs to allow the memory of a punishment to fade over time.This contrasts with the Game Theory approach of examining the rational decision for di erent fixed probability values. .
The ABM is presented in two steps.The first is a discussion of an implementation that, like Game Theory, focusses only on information obtained through direct experience; perceived probability of punishment is high immediately a er being punished but reduces over time.The model is then extended to allow the entrepreneur's decision to comply or resist an extorter to also depend on events in their neighbourhood.This model is an intuitive implementation of reputation for the Mafia.The neighbourhood model requires much lower levels of punishment, which is more consistent with real life extortion racket phenomena.
. This paper is structured as follows: In Section we discuss major game theoretic approaches to extortion rackets (developed in Konrad and Skaperdas ; Gambetta ; Smith and Varese ).In Section we discuss existing agent-based models of extortion and related dynamics, such as reputation and deterrence.In Section an agent-based model inspired by the game theoretic framework from Section is presented and analysed.In Section this agent-based model is extended to incorporate social aspects of Mafia reputation and the two approaches compared.In Section we conclude and discuss future work.

Game Theoretic Approaches to Extortion Rackets
. The extortion situation intuitively reads as an iterated decision tree.The extorter demands money from an entrepreneur, the entrepreneur decides to pay or not to pay, and then the extorter decides whether to punish.The demand and decision occurs multiple times between a paired extorter and entrepreneur.In the game theoretic literature on extortion rackets (Konrad and Skaperdas ; Gambetta , ; Varese , ), the payment decision depends on the entrepreneur's expectation of being punished for refusal to pay.If the payment demand is smaller than the expected loss from damage (that is, the probability of punishment multiplied by the damage cost), the entrepreneur will pay the extorter.Usually protection demands are small and punishments potentially very high (such as arson attacks on the shop taking away the livelihood).This means the important variable to assess for the entrepreneur is the probability of being punished.Two broad approaches can be distinguished in the literature.

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The first approach (Konrad and Skaperdas ) treats the probability of punishment as endogenous, arising from the e orts invested by extorters and police.The game described in (Konrad and Skaperdas ) formalises the interdependent choice between the three actors: the extorter, the entrepreneur and the police.The approach sets out to find equilibria for investment into punishment by extorters and e orts by the police to undermine extortion.Entrepreneurs simply calculate the payo of compliance or resistance, given levels of police presence and e ort compared to extorter aggression.

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On the other hand, (Gambetta ; Smith and Varese ) have levels of police presence as an exogenous variable, focussing instead on the extorter-victim interaction.The game originates with (Gambetta ) who uses it as a setting to discuss reputation, signalling and piracy of symbols.Extorters are split into two types, the real Mafiosi and fakers.Mafiosi establish a reputation for punishing resistance and fakers can free-ride on this reputation if they manage to signal as belonging to the real Mafia.Entrepreneurs decide whether to pay or not depending on their individual expected punishment probability calculated from whether they think an extorter is a faker or not, given knowledge of the level of police presence.High police presence lowers the probability of a Mafioso to punish and also the probability of fakers to extort.

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The game has been formally analysed in detail in (Smith and Varese ).Police presence is either high or low, determined probabilistically.From the construction of the various risks and costs, both Mafiosi and fakers demand in some situations, but only Mafiosi punish resistance and only when police presence is low.

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The single iteration Mafia-faker game results in three equilibria.Region describes situations with a high probability of high police presence.Entrepreneurs never pay as they feel safe from punishment due to the high police presence.Thus, fakers do not even attempt extortion as there is no benefit.Only Mafiosi demand, and they only punish refusal when police presence is low (a low probability occurrence).Region has a lower probability of high police presence and hence higher probability that refusal will result in punishment if the extorter is a Mafioso.In this region, the cost of punishment to the entrepreneur is high and entrepreneurs believe that extorters are (mostly) Mafiosi, so they pay the relatively small demands of all extorters.This provides an opportunity for fakers to free-ride on the Mafia reputation and the incentives for fakers partly depend on the risk of encroaching on Mafia territory.As entrepreneurs always pay, they are unable to use their own experience to recognise whether extorters are real Mafiosi.
. Region is characterised by uncertainty and leads to the most interesting behaviour.While Mafiosi always demand, fakers also demand sometimes.Entrepreneurs pay sometimes, depending on the interplay of their belief that an extorter is a faker and the levels of police presence.Refusal only leads to punishment where the extorter is a Mafioso and police presence is low.Fakers are more likely to make demands when their expectation of being paid is higher; because entrepreneurs believe that extorters are Mafiosi, police presence is low (so there is risk of punishment) or demand amount is small (so lower cost than the risk of punishment).
. These regions are also important in describing the repeated version of the game, analysed in detail in (Smith and Varese ) and the inspiration for the ABM presented here.While the three regions are substantially similar to the single iteration situation, behaviour near the borders is changed once future interactions are also considered.In particular, there is a stronger incentive for Mafiosi and fakers to extort and punish, and a stronger incentive for entrepreneurs to reject the demands.However, entrepreneurs also recognise the stronger incentive for extorters to punish, which creates a countering influence to pay.For extorters, the expensive decision to risk detection (by police or Mafia for fakers, or by police for Mafia) is potentially repaid with two payments.For entrepreneurs, the risk of punishment for refusal is being judged against the cost of two payments.That is, an expensive risk is spread because it establishes behaviour for two turns, or acts as a "signal of type" (Smith and Varese , pg ).Instead of the three regions, these competing incentives lead to six equilibria in the two iteration game.In contrast with the single turn game, even fakers will punish a refusal in one of the regions.

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As well as identifying these equilibria, (Smith and Varese ) noted counterintuitive results concerning levels of violence.In particular, violence is a sign of incomplete control by the Mafia; violence only occurs where entrepreneurs refuse a demand.This may arise either because they know police presence is generally high (region ) or believe the extorter could be a faker (region ).With low police presence, there is no violence once the Mafia has established control (by eliminating fakers).Violence then erupts from shocks to the system, such as changes in police presence or the size of demands.

Agent-Based Modelling Approaches to Extortion Racketeering
. In this paper we develop an ABM of extortion racketeering using the Mafiosi-faker game described above as a conceptual base.
. There are three published ABMs directly concerning extortion racket dynamics.Sonzogni et al. ( ) presents a model to investigate the social and economic influences on extortion of entrepreneurs, recruitment to a criminal organisation and judicial punishment on the social entrenchment of extortion rackets.It includes individual labour market conditions and risk perception, combined with a social influence mechanism based on imitating economic success.The model is used to investigate the combined e ect of state punishment of, and recruitment to, a criminal organisation.

Nardin (
) describes a model focussed on extortion racketeering in Sicily and southern Italy.Based on the cognitive agent architecture Emil-A, developed to understand normative behaviour, the model represents in particular cultural dimensions of extortion racketeering.It explicitly investigates a change in culture in Italy of both law enforcement and bottom-up behaviour change through normative communication.
. Troitzsch ( , ) presents a model to investigate the e ects of extortion racketeering on the distribution of wealth in society and the interactions between state, civil society and criminal organisations regarding compliance, resistance, denunciation and prosecution of criminals.Law enforcement plays a major role in this model as policemen are in charge of arresting Mafiosi and interact with entrepreneurs that denounce extortion.The model simulates e ects of extortion racket at the systems level, using thresholds and probabilities.This implementation allows a systematic exploration of the parameters potentially relevant to an extortion racket, such as propensity to pay.The model suggests that the main influence on the success of an extortion racket is the effectiveness of prosecution of extorters by the state, followed by the probability of victims to denounce extorters.

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Agent-based modelling has also been used to examine deterrence in social compliance phenomena more generally, outside of the extortion racket application.Mafia punishment to induce payment through fear is a specific application of deterrence models, which have been widely used in ABM, for example to engender pro-social behaviour with utility maximising agents in models of social norms (Elsenbroich and Gilbert , Chapter ).ABM has implemented deterrence with punishment in a variety of ways, with di erent punishment structures (e.g.central or distributed) and various cognitive mechanisms (e.g.memory of past experiences or perceiving whether others are punished).

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A model of tax evasion developed and analysed in (van Baal ) includes punishment in a way that is most similar to its role in extortion dynamics as we discuss here.The model uses the cellular automata approach, with each location on a grid representing one agent.Agents situated next to each other are neighbours and in each others' social networks.At each step, agents decide whether to evade tax or not.Tax evasion without getting caught has a positive payo , while norm compliance has a payo of zero and being found out to evade tax is sanctioned by a negative payo (a cost).A law enforcement agency checks agents at random, representing the probability of getting caught through audit.The agent bases its decision on whether the expected payo of crime is greater than the expected payo for compliance.The expected payo is calculated, following Becker ( ), by weighing the potential payo of transgression against the probability and cost of getting caught.
. Agents commit a crime if they perceive crime as profitable.The payo and cost of transgression is known to the agent.The probability of being audited is estimated by the agent from its social network.The model shows that higher sanctions and higher audit probabilities lead to higher levels of compliance.
. This paper draws on the game theoretic and ABM deterrence literatures to operationalise a Mafia-faker conceptual framework for ABM.The narrative of the Italian Mafia is transferred from the original game theory article (Smith and Varese ( )) and what our model sets out to show is that a model of an extortion racket that does not take into account the neighbourhood e ects on deterrence (and Mafia reputation by proxy) misses one of the most important aspects of extortion racketeering.The model allows for a detailed analysis of the role of punishment to be extended to a community setting, where entrepreneurs learn from the experience of others, as well as their own.

An Agent-Based Model of the Mafia-Faker-Game
. We present an ABM of the interaction game between Mafiosi, fakers and entrepreneurs.The model consists of two kinds of agents: extorters and entrepreneurs.Extorters can be real Mafiosi or fakers.The di erence between Mafiosi and fakers is that Mafiosi punish resistance whereas fakers, whilst making extortion demands just like Mafiosi, do not punish.Police presence is deliberately le out of this model as it is an exogenous influence on punishment probability (following Smith and Varese ) rather than an active agent.This means the model focusses on the equilibrium regions in which entrepreneurs make decisions uncertain of the situation (Regions and in Section ).
. Entrepreneurs are the targets of extortion demands by both fakers and Mafiosi.Extorted entrepreneurs decide in each simulation step whether they pay the pizzo (the amount of the payment requested) or start resisting.An ABM to model the dynamics of extortion rackets needs to implement the conditions under which entrepreneurs pay or resist (decision mechanism), punishment of an entrepreneur by the Mafia in case of resistance and how this punishment influences an entrepreneur's future decision making.Consequently, factors to be operationalised include an extorter's reputation to punish and the entrepreneur's fear.
. If all extorters are real Mafiosi (and police are ine ective), anyone approached should pay as punishment costs exceeds the pizzo and the probability of punishment is very high.In the game theoretic analysis the faker introduces incomplete knowledge into the game (Gambetta ), replacing the certainty of being punished with a probability.This probability is the essential feature of the Mafia-faker game.The decisions of the entrepreneurs depend on how they assess the probability of being punished and the expected damages arising from punishment by the Mafia.

Decision:
If pP × D ≥ E, pay otherwise, refuse, ( ) where pP is the probability of punishment, D the size of the possible damage caused by punishment and E the size of the pizzo.
. Game theory itself does not provide a cognitive mechanism through which an agent might obtain the punishment probability.Instead, expected behaviour is presented for di erent regions of the probability space.If the agent assesses the probability at some value, it adopts a specific behaviour (pay or resist) based on that assessment.The adopted behaviour is the option calculated to maximise the expected payo , the probability of an outcome multiplied by the payo of that outcome for each behaviour choice.
. In an ABM, the agent perceives its environment and chooses a behaviour based on a combination of that environment and its own characteristics.In the model presented here, the perceived punishment probability is determined by an entrepreneur's past experience on refusing to pay.If the refused extorter is a Mafioso, the entrepreneur may get punished, if it is a faker, there will be no punishment.If an entrepreneur is punished, its perceived punishment probability becomes .This is then divided by .(representing a decay of 0.09) each step the entrepreneur is not punished as the agent 'forgets' about the trauma of being punished and increasingly wishes to reassess the situation.Input parameters in this model are the territory of an extorter (the extorterradius), some financial inputs (the amount of money requested (pizzo) and the damaged incurred by an entrepreneur if it is punished (damages)), the overall number of entrepreneurs and the number of Mafiosi and fakers.
. One additional input needs to be discussed in a little more detail.The ability of Mafiosi to punish resistant entrepreneurs is dependent on the wealth of the Mafia being in excess of the cost of punishing.In the experiments the cost is varied at , and .Although a punishment has some actual monetary cost associated, like the gasoline needed for the arson attack, the cost represents the disutility associated with the risk of being arrested by the police.Thus a level of means the Mafia has almost total impunity, means there is some cost associated and stands for a relatively high level of authority interference.These particular values were chosen to demonstrate di erent patterns in the model results.At , punishment is regular but not constant, and Mafiosi were successfully undermined at (corresponding to high police presence).
. The model is initialised with entrepreneurs randomly located on a 33×33 grid.The appropriate number of extorters are located in a fixed circle of radius around the centre of the grid.The extorter-radius determines the area of each extorter's territory.Territories overlap, but each entrepreneur is extorted by at most one extorter.Extorters are initialised with units of capital.Entrepreneurs have a monthly income, normally distributed with a mean of and a standard deviation of .Every time steps entrepreneurs are paid their monthly income and extorters are paid their pizzo by the entrepreneurs they extort.

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Every time step, each extorter chooses a random entrepreneur within their territory and if the entrepreneur is not already extorted, they make an extortion request (if the entrepreneur is already extorted nothing happens).
In response, the entrepreneur decides whether to pay.In addition, entrepreneurs who are already being extorted reassess whether they will continue to pay.In both cases, the decision to pay is based on the expected probability of punishment as described at Equation above.If the extorter is a Mafioso and has su icient resources, it chooses an entrepreneur to punish from those resisting.
. Experimentation focusses on the analysis of how the extorter radius and ratio of Mafiosi or fakers together influence levels of resistance and the number of punishments.The financial inputs are kept constant, the pizzo at and the potential damages an entrepreneur expects at , , .We vary the number of extorters overall, the ratio of Mafiosi and fakers, the extorter radius and, as discussed above, the cost of punishment for the Mafia.

Results and Analysis
. Analysis focussed on how resistance and punishment are influenced by changes in the extorter population, extorter radius, and cost of punishment.To eliminate run-in e ects, model results ignore the first time steps and are reported as the average value over the following time steps.
. The model produces a broad range of levels of resistance, from % to % of entrepreneurs approached by extorters.Resistance is clearly related to the extorter radius, cost of punishment for the Mafia and the presence of fakers (see Figures and ).A full interpretation also relies on the interplay between levels of resistance and punishment.

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Focussing on the Mafia only scenarios (Figure ), as the cost of punishment increases and their territory expands, the Mafia have too few resources to retain control and resistance increases.With a punishment cost of , each punishment consumes the resources obtained from acquiescent entrepreneurs and there is insu icient revenue to regularly punish resisters.Unpunished resistance leads to lower revenue and worsens the problem (from the Mafia perspective), with the consequent overall behaviour of no punishment and total resistance for .
The presence of fakers increases entrepreneur resistance and, for the scenarios with punishment cost of , increases the punishments that must be made by the Mafia (Figure ).The increased resistance is straightforward, many entrepreneurs are in the territory of fakers but not Mafia and, once they realise they are not being punished, they continue to resist.

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The punishment e ect is more interesting.The introduction of fakers makes no di erence in the number of punishments per Mafioso per time step where the punishment cost is or , .At a cost of , Mafia are able to punish whenever they like and adding fakers does not change the frequency they need to punish to maintain control.At a cost of , , Mafia do not have the resources to punish once their initial allocation has been consumed and adding fakers does not add to their resources so they are also unable to punish in the faker scenarios.

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The additional punishments in the faker scenarios for punishment cost of arise from the particular interaction of entrepreneur density and di erent financial elements in the experiments.The combination of decay rate (1 − 1 1.1 ) in assessment of punishment probability, pizzo size ( ) and damages arising from punishment ( , , ) means that an entrepreneur resists time steps a er being punished (by equation ), during which time they make (or sometimes ) payments and therefore generally provide su icient resources to pay for only one punishment.Having been punished, the extorter will acquiesce the next time they are approached and will continue to pay for the remainder of time steps a er the punishment.With di erent parameter variables, the same behaviour would occur but at a di erent punishment cost.The general principle is that at a moderate punishment cost, the territory of each Mafioso must be small enough to support regular revisits.For the Mafia only scenarios, the territory is too large once extorter radius reaches , and financial resources constrain the number of punishments (compare cost cells to cost cells at Figure right).However, when sharing entrepreneurs with fakers, the Mafia territories are reduced and they have su icient resources to punish whenever .The model we have presented recreates some of the results of the game theoretic model.In particular, resistance is high when there is a high punishment cost (equivalent to high police presence) and, at lower punishment cost, resistance increases as the proportion of fakers increases.In addition, violence (punishment) increases as the Mafia try to exert control over a greater number of entrepreneurs.However this model falls short of replicating one of the most stable stylised facts of extortion rackets: high levels of compliance with low levels of punishment.This combination only occurs for small extorter territories.In this model, deterrence of entrepreneurs is implemented in a purely individualistic way using their memory of being punished, and the Mafia must immediately punish resisters to keep control of a territory.This is costly and leads to Mafiosi 'running out of resources' and loss of control.In the next section, we extend the model to implement a reputation mechanism for Mafiosi.

An Agent-Based Model of Mafia Reputation
. The presented ABM applies a strongly individualistic interpretation of deterrence, chosen to stay as close as possible to the game theoretic model of Smith and Varese ( ).In this section we develop an ABM that allows entrepreneurs to also gain information from the experience of their neighbours.That is, an entrepreneur is not only deterred by what happened to him or herself but also by experiences of others nearby.The individualistic memory based calculation of the punishment probability does not take this social aspect of deterrence into account.

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In the extended model, the memory based calculation is replaced by a mechanism where the punishment probability is determined by the observation of punishment of others as well as personal experience.If an entrepreneur observes a punishment in a certain neighbourhood, its perceived punishment probability becomes , decaying each step the entrepreneur does not observe a punishment.The input parameters in this model are the same as above, i.e. extorter-radius, pizzo, damages and cost of punishment, number of Mafiosi, number of fakers, number of entrepreneurs, but in addition entrepreneurs have a neighbourhood-radius, determining the size of the neighbourhood in which observed punishments a ect their perceived punishment probability.

Figure :
The two figures represent a situation with one Mafioso, two fakers (purple and grey large dots) and two entrepreneurs (small dots).The memory-dependent punishment probability is shown in (a) and the extended model with neighbourhood e ects in (b).The circles around them visualise the extorter radius and (in (b)) neighbourhood radius.Red entrepreneurs pay the pizzo, green entrepreneurs resist paying.For the memory model (a), the red entrepreneur might be paying the faker because it is in the intersection of the real Mafioso and the faker, and has been punished previously by the Mafioso, but the green entrepreneur will always resist as it will not personally experience punishment.For the neighbourhood model (b), the Mafioso punishment is within the neighbourhood radius (large circle) of the isolated faker and can therefore provide a deterrence e ect on the entrepreneur that would have resisted in the memory model.This provides an extended reach of the deterrent e ect from the punishments of the real Mafioso and hence free-riding by appropriately located fakers.The neighbourhood based calculation is expected to enhance the deterrence of each punishment as it not only deters the punished entrepreneur but also those in that are closer than the neighbourhood radius (see Figure ).This socially enhanced deterrence of punishments should lead to: . lower levels of resistance, in particular as the neighbourhood radius increases; . lower levels of punishment for similar levels of resistance; and . easier free-riding for fakers on the Mafia's reputation.
. We run similar scenarios as in the memory case discussed in Section but, in addition to varying the extorterradius, we also vary the neighbourhood-radius. Punishment cost is set to , for all experiments, which is the value at which the previous model had no punishments and fully resistant entrepreneurs because the Mafia had insu icient resources to maintain control.

Results and Analysis
. As for Section , the presented results are the average value over , time steps, a er discarding the first to eliminate run in e ects.In figures and , the , punishment cost scenarios had full resistance (yellow) and no punishments (blue) for all extorter combination and extorter radius combinations (top lines of each panel).In the extended model (figures and ), this same pattern is observed for neighbourhood radius up to , but begins to break down as neighbourhood radius increases. .
For the Mafia only scenarios (Figure ), the constraining factor is the resources available for punishment, as can be seen by the existence of at least some resistance combined with punishment levels below .This constraint controls the model behaviour; a larger extorter territory allows greater revenue but also requires more punishments.As the neighbourhood radius increases, each punishment potentially influences the behaviour of a larger number of entrepreneurs and therefore allows control over a greater territory.
. For the particular experiment values, resistance generally decreases as the number of Mafiosi increases.However, this is not true for extorter radius of , where resistance is high for the and Mafiosi scenarios and lower for the and scenarios.At and Mafiosi, there are too few entrepreneurs in each territory to provide resources for punishment because the territories are, respectively, too small or too overlapping.
. For all Mafia only scenarios, resistance decreases and punishment increases as extorter radius increases, and resistance decreases with little change in punishment as neighbourhood radius increases.As extorter radius increases for a fixed neighbourhood size, the pizzo revenue increases and enables more punishment.Provided the entrepreneurs are able to observe su icient nearby punishments (neighbourhood radius of at least ), these punishments induce enough acquiescence to fund further punishments.As neighbourhood radius increases for a fixed extorter territory, each punishment is observed by more entrepreneurs and resistance decreases, which increases extorter revenue and funds a small increase in punishments.
. A di erent pattern emerges where the Mafia don't need to rely on multiple entrepreneurs to provide the resources for punishment.With punishment cost set to , the number of punishments consistently decreases as the neighbourhood increases (Figure , right).That is, the need to punish consistently decreases if there is no resource constraint.Resistance shows a di erent pattern, decreasing for initial increases in neighbourhood size, but then increasing where the neighbourhood radius is larger than the extorter radius (Figure , le ).This increase arises because all the entrepreneurs are influenced by the same punishment and thus become resistant again in the same time step.Where there are few (and therefore distant) extorters, the synchrony leads to high resistance at regular time steps, which is resolved with a single punishment on each occasion.

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As with the initial model, the presence of fakers increases entrepreneur resistance but there is no e ect on punishment levels compared to the Mafia only scenarios (Figure ).Some entrepreneurs are in the territory of fakers but not Mafia and, if their neighbourhood radius does not extend to the Mafia territory, they cannot observe punishments and continue to resist.As the neighbourhood radius increases, there is a smaller di erence between the Mafia only and mixed Mafia / faker scenarios.
. One consequence of the Mafia punishing in the mixed Mafia and faker scenarios is that entrepreneurs may acquiesce to a faker's extortion attempt.As fakers do not bear the cost of punishment, fakers who successfully use the Mafia's reputation to extort can accumulate greater wealth than Mafia.At time step , , the average wealth of fakers is between .and .times that of the Mafia.This ratio increases as extorter radius increases but has no clear relationship with neighbourhood radius (Figure ).

Conclusion and Future Work
. We have presented two ABMs of extortion rackets inspired by the game theoretic analysis of extortion by Gambetta ( ) and Smith and Varese ( ).This approach uses a three player game consisting of a Mafioso, a faker and an entrepreneur, with the latter having some belief about probability of being punished for resisting extorter attempts.The analysis identified regions of punishment probability space with di erent entrepreneur decisions about resisting and extorter decisions to punish.A key result is that there are regions with high compliance and low punishment, with high levels of violence indicating loss of Mafia control.However, the game theory framework does not provide a mechanism by which entrepreneurs can assess punishment probability, it is exogenous.

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The ABM were implemented with the same three active kinds of agents; Mafiosi, fakers and entrepreneurs.The entrepreneur decision-mechanism calculates the utility of complying or resisting, determined by the entrepreneur's belief about the probability of being punished and the impact of the punishment.  .
In the first model the punishment probability belief is calculated using a memory based mechanism; if an extorter is punished, it will have a high punishment probability, slowly decreasing over time.The model recreated most of the game theoretic results, showing how increasing punishment is a sign of Mafia weakness and also showed the detrimental e ect fakers have on the Mafia reputation.It failed, however, to recreate one of the most stable stylised fact of extortion rackets: the combination of low levels of resistance and low levels of punishment.In order to achieve low resistance levels Mafiosi had to punish constantly.Further, if punishment is costly (representing risk of police detection), the Mafia may collect insu icient resources from the acquiescent entrepreneurs to punish the resisters and a spiral of increasing resistance occurs.
. We then extended the memory based ABM by an alternative decision-mechanism based on observing punishments in the neighbourhood rather than only relying on personal experience.This model implements some social aspects of deterrence and reputation through social amplification Kasperson et al. ( ) of the e ect of each punishment.This model resulted in much more realistic extortion behaviour, where low levels of resistance are paired with low levels of punishment.

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Although the memory mechanisms leads to results with high levels of acquiescence, it is clear that social transmission of reputation renders punishment much more e ective.One consequence of this extension, however, is that fakers who are su iciently close to a Mafioso are able to take advantage of the Mafia propensity to punish and extort without the cost of punishing.Even with non-overlapping extorter radii, if the neighbourhood observation radius is large enough, fakers can survive in the shadow of the Mafia.
. The models presented are quite simple and abstract, but allow the exploration of some fundamental dynamics of punishment, reputation and resistance.They suggest that some form of reputation is required in order to achieve compliance without substantial punishment.In future work we will implement extensions on the same level of abstraction that examine di erent social structures in which the agents operate.In particular we will investigate ways in which extortion rackets can be undermined or fought by both bottom up strategies, such as normative reasoning and collective reasoning spreading resistance and top down interventions such as police pressure and surveillance.

Figure :
Figure : Proportion of entrepreneurs resisting extortion attempts (le ) and the proportion of Mafia who punish (right).Each panel presents the results for one of the four Mafia only scenarios, with , , or Mafiosi extorting (Mafia M F , Mafia M F , Mafia M F and Mafia M F respectively) and presents the average results over , time steps for simulations that vary by cost of punishment and the radius of extorter territories.

Figure :
Figure : Proportion of entrepreneurs resisting extortion attempts (le ) and the proportion of Mafia who punish (right).Each panel presents the results for one of the four scenarios with extorters, with , , or Mafiosi extorting and the remainder fakers (Mafia M F , Mafia M F , Mafia M F and Mafia M F respectively) and presents the average results over , time steps for simulations that vary by cost of punishment and the radius of extorter territories.

Figure :
Figure : Proportion of entrepreneurs resisting extortion attempts (le ) and the proportion of Mafia who punish (right).Each panel presents the results for one of the four Mafia only scenarios, with , , or Mafiosi extorting (Mafia M F , Mafia M F , Mafia M F and Mafia M F respectively) and presents the average results over , time steps for simulations that vary by neighbourhood radius (the distance over which an entrepreneur can observe punishments) and the radius of extorter territories.The punishment cost is fixed at , , which is the same value for the top row of each panel in Figure .

Figure :
Figure : Proportion of entrepreneurs resisting extortion attempts (le ) and the proportion of Mafia who punish (right).The punishment cost is fixed at , which allows Mafiosi to punish every time step if appropriate.Both the original model (neighbourhood radius = ) and the extended model (neighbourhood radius > ) are presented.Each panel presents the results for one of the four Mafia only scenarios, with , , or Mafiosi extorting (Mafia M F , Mafia M F , Mafia M F and Mafia M F respectively) and presents the average results over , time steps for simulations that vary by neighbourhood radius and the radius of extorter territories.

Figure :
Figure : Proportion of entrepreneurs resisting extortion attempts (le ) and the proportion of Mafia who punish (right).Each panel presents the results for one of the four scenarios with extorters, with , , or Mafiosi extorting and the remainder fakers (Mafia M F , Mafia M F and Mafia M F and Mafia M F respectively) and presents the average results over , time steps for simulations that vary by neighbourhood radius (the distance over which an entrepreneur can observe punishments) and the radius of extorter territories.The punishment cost is fixed at , , which is the same value for the top row of each panel in Figure .

Figure :
Figure : The average faker wealth divided by the average Mafioso wealth at time step , .Both the original model (neighbourhood radius = ) and the extended model (neighbourhood radius > ) are presented.Each panel presents the results for one of the three scenarios with extorters, with , or Mafiosi extorting and the remainder fakers (Mafia M F , Mafia M F and Mafia M F respectively).
Table describes the parameter combinations, with simulations.
Table describes the parameter combinations, with simulations.