Some real-time electricity markets use a rolling horizon approach to clear supply and demand. Using a model of a rolling horizon market, this paper analyzes the incentives of market participants to place bids for future time-periods that are consistent with what they intend to bid for the same time-period in later market clearings. We show that a market participant with market power has financial incentives to bid inconsistently, and that some inconsistencies persist even if the outcomes from all time-periods are financially settled in every market clearing.