Crime as a phenomena exhibits spatial variance that is both large and persistent. This paper explains that variance by constructing a model of criminal behavior in which group or neighborhood behavior exists in one of multiple equilibriums. This binomial discrete choice model incorporates the concept of social interactions into previous models of crime by including the effect of criminal activity in a neighborhood on a resident's criminal behavior. Analysis of social interactions between individuals defines an aggregate interaction to simplify a multi-body problem into a single-body problem. Equilibrium is determined by private incentives, the degree of social interactions, and the unobserved heterogeneity among the actors. Equilibrium is derived using Brouwer’s fixed point theorem for simplotopes; Brouwer’s fixed point theorem is in turn proved through the use of Sperner’s Lemma. The degree of social interactions present in Chicago neighborhoods with regards to both violent and property crime is also measured through a logistic regression analysis. Significant social interactions effect was found with regard to motor vehicle theft, theft, burglary, assault, and robbery. Rather than viewing social and economic explanations of crime as incompatible, the model integrates other criminological theories into the rational actor framework.


Burnell, James

Second Advisor

Hartman, James


Mathematics; Economics

Publication Date


Degree Granted

Bachelor of Arts

Document Type

Senior Independent Study Thesis



© Copyright 2015 Daniel Patrick Miller