The recent Wolak report on the New Zealand electricity market found evidence of substantial market power. The report, an empirical one, was heavily criticised on several aspects of its methodology. We investigate market power in the New Zealand Electricity Market during 2006 and 2008 using an alternative methodology; a computer agent-based model. With this model, we can account for all the substantive criticisms of the Wolak report. Our results are broadly in line with those of Wolak, nonetheless there are significant differences. In particular, our allocation of market rents across periods is very different. We estimate total market rents for 2006 and 2008 to be $2.6 billion.