Crime in Equilibrium

Abstract

The Port of Rotterdam is the biggest port in Europe and with its great location an important place for trade between Europe and other continents. Record numbers of intercepted illegal goods show that criminals use this port to traffic illegal goods. A lot is still unknown about the criminal supply chain in the Port of Rotterdam and about the chance to catch illegal goods that are smuggled. Therefore this research provides insights into this criminal supply chain by looking into the effects of the distribution of resources by law enforcement agencies between methods that can be used to catch illegal goods on the chance to catch illegal goods. This research looks at the criminal supply chain from South America to the Port of Rotterdam where it focuses on the smuggling methods used inside the Europe Container Terminals in the Port of Rotterdam. Criminals make use of four smuggling methods which are the pincode fraud method, the switch and pincode fraud method, the extraction method and the empty depot method. Law enforcement agencies have a scan and a surveillance method to catch illegal goods. The methods of law enforcement agencies can catch different smuggling methods and both have a chance to catch illegal goods smuggled with the empty depot method. Whereas criminals choose per illegal container which smuggling method will be used, this is not possible for law enforcement agencies. Therefore, a linear relationship between the part of resources appointed to a method and the accuracy of that method is assumed for the methods of law enforcement agencies. An agent-based model is built to capture the complexity of this criminal supply chain and show the behaviour of the cat-and-mouse-like situation between criminals and law enforcement agencies. This agent-based model is combined with the Nash equilibrium known from game theory, as game theory can give insights into this situation using a mathematical framework. As these research methods have not been combined for the distribution of resources among methods in the Port of Rotterdam in earlier research, this research provides insights into how these research methods can be combined and whether they will provide similar results. When combining the Nash equilibrium from game theory with the agent-based model it is expected that the distribution of resources for the two players, criminals and law enforcement agencies, in the agent-based model will eventually end up in or around the Nash equilibrium. This is because, in the Nash equilibrium, no player can get a higher expected payoff by deviating from the equilibrium. The players in the agent-based model update their distribution of resources every period of four weeks to adapt to the behaviour of the other player. This adaption is modelled with an updating rule. As literature indicated that the modelling of this updating rule can cause different behaviour in agent-based models, six different updating rules are tested in this research. Given a chance to catch illegal goods of the scan of 0.18 for smuggling methods that can be caught by the scan and a chance of 0.8 for surveillance for methods that can be caught by surveillance, the Nash equilibrium is reached when law enforcement agencies appoint 40/49 of their resources to the scan and 9/49 to surveillance and criminals appoint 40/49 of their resources to the pincode fraud method and 9/49 to the switch and pincode fraud method and the extraction method combined. In the Nash equilibrium criminals will not appoint any resources to the empty depot method. The six updating rules used in the agent-based model show different behaviours. Some updating rules cause the players in the agent-based model to appoint all their resources to only one method and others cause the players to end up in a cyclic pattern around the Nash equilibrium. The agent-based model also shows that by changing parameters of certain updating rules, the behaviour can change completely. For some updating rules the distribution of resources can get appointed according to an equilibrium which is not a Nash equilibrium as the payoffs of the methods are not equal to each other. Various difficulties arise when designing an updating rule. None of the six updating rules can guarantee the agent-based models to end up in or around the Nash equilibrium. These difficulties include that resources should be distributed according to the payoff of methods according to game theory and should not be done according to the success rate of methods. Other difficulties arise when methods get appointed little or no resources. As it is the best response for players to distribute all their resources to one method when the other player is not playing according to the Nash equilibrium, the updating rule needs to be able to appoint zero resources to a method. Updating rules should also ensure that this method can be reappointed more resources when the other player changes its distribution of resources. Other difficulties include equilibria that are not a Nash equilibrium as mentioned above and the fact that players do not adapt in the same way when they do not have the same number of methods. From this research, it can be concluded that in order to use an agent-based model for the situation between law enforcement agencies and criminals the knowledge about Nash equilibria should be considered while creating the model. This will not happen automatically as seen by the multiple difficulties this research showed. This research also shows that updating the distribution of resources by law enforcement agencies is important as they risk having an unnecessarily low chance to catch illegal goods when criminals adapt, while law enforcement agencies would not. Therefore, it is recommended for law enforcement agencies to update the distribution of resources when it is expected that criminals will adapt as well, to not risk having an unnecessarily low chance of catching illegal goods. Furthermore, it is recommended to consider the Nash equilibrium while updating the distribution of resources and to carefully observe the distribution of resources of criminals when appointing all resources to only one method. Limitations of this research include that there are only a limited number of methods included and players can not learn new methods. Due to the limited data about the criminal supply chain and about the methods that can be used by law enforcement agencies, there is deep uncertainty in model parameters, especially in the chances of catching illegal goods of the methods of law enforcement agencies. Therefore the results are not entirely valid and should only be used to analyse expected behaviour. Further research is needed on these chances of catching illegal goods and to test more updating rules as this research does not provide an updating rule that will ensure that an agent-based model will always end up in or around the Nash equilibrium.