This thesis examines the behaviour of retail petroleum markets, with a case study examining prices in Perth, Australia. The aim of the thesis is two-fold. Firstly, it aims to extend the Edgeworth Cycles literature by showing how a simple, distance-based model of duopolistic competition can give rise to Edgeworth Cycles. Secondly, it makes use of the results of this model to build a model of the structure of the Perth market and to explore competition in that network. In the empirical component of the thesis, I explore whether network structure influences both the prices charged by each retail petroleum outlet and the shape of price cycles exhibited by each retail petroleum outlet. In addition, having performed a spectral analysis on prices and finding that most retail petroleum outlets do not follow a single cycle, but in fact use cycles of differing lengths, mostly seven and ten-day cycles, I explore whether network structure influences these choices or not. In the empirical analysis, I find evidence that network structure does, in fact, influence both price and the nature of cycles.