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Modelling these costs and constraints requires integer formulation of the units, and so they have typically been ignored in electricity market modelling and simulation to date. We present a stochastic equilibrium model to include these costs and constraints in a Cournot game. We solve it using the Gauss-Seidel diagonalization algorithm and apply it to a model of the power system of the island of Ireland for varying levels of variable renewable power generation. We find that the impacts of integer modelling are non-trivial, and are heterogeneous across firms and wind levels. Furthermore, excluding integer modelling exaggerates the impact of price-making behaviour. 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