Crime in Game Theoretic Models: An exploration of the rational criminal in a variety of frameworks

There is as much contention over the cause of crime as there is about how to solve it, and the two issues are inextricable from one another. While the idea of studying such a deeply social and humanistic issue through the ‘cold lens’ of mathematics may seem unorthodox or even unproductive to the layperson, the practice has become commonplace since Gary Becker’s introduction of the ‘rational criminal’ model in his paper Crime and Punishment: An Economic Approach in 1968. The rational criminal model is a method of explaining the actions of a criminal not by attributing them to an inherent mental difference or deficiency, nor by some product of social repression, but as decisions to be calculated in the same manner as all economic choices: a rational consideration of the costs and benefits of committing such an action. That this seems a natural way of looking at crime in the present day is a testament to its effectiveness in understanding some aspects of crime, as it was by no means orthodox when it was first proposed; the dominant view prior to Becker’s contribution was that criminals were produced by a combination of mental deficiency/illness and social oppression. Since this model entered the mainstream, the field of economics has subsumed many areas of crime research, and indeed a variety of other societal phenomena which would have previously been claimed by sociology or psychology. This paper will focus on the prevention aspect: What methods are most effective in preventing or reducing crime, and what approaches have we yet to study? The methodology of the paper is as follows: First, a simple game is introduced in which rational actors use Bayesian Inference to decide whether or not to commit a crime. This game is then modified by adding a false arrest component. Secondly, a simulation of a pure coordination game is constructed, in order to determine the effectiveness of an unrelated choreographer at producing and maintaining certain equilibria