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Market power behaviour often occurs in modern wholesale electricity markets. Mixed Complementarity Problems (MCPs) have been typically used for computational modelling of market power when it is characterised by an oligopoly with competitive fringe. However, such models can lead to myopic and contradictory behaviour. Previous works in the literature have suggested using conjectural variations to overcome this modelling issue. We first show however, that an oligopoly with competitive fringe where all firms have investment decisions, will also lead to myopic and contradictory behaviour when modelled using conjectural variations. Consequently, we develop an Equilibrium Problem with Equilibrium Constraints (EPEC) to model such an electricity market structure. The EPEC models two types of players: price-making firms, who have market power, and price-taking firms, who do not. In addition to generation decisions, all firms have endogenous investment decisions for multiple new generating technologies. The results indicate that, when modelling an oligopoly with a competitive fringe and generation investment decisions, an EPEC model can represent a more realistic market structure and overcome the myopic behaviour observed in MCPs. The EPEC considered found multiple equilibria for investment decisions and firms' profits. However, market prices and consumer costs were found to remain relatively constant across the equilibria. In addition, the model shows how it may be optimal for price-making firms to occasionally sell some of their electricity below marginal cost in order to de-incentivize price-taking firms from investing further into the market. Such strategic behaviour would not be captured by MCP or cost-minimisation models.