Unique supply function equilibrium with capacity constraints

Consider a market where producers submit supply functions to a procurement auction with uncertain demand, e.g. an electricity auction. In the Supply Function Equilibrium (SFE), every firm commits to the supply function that maximises expected profit in the one-shot game given the supply functions of competitors. A basic weakness of the SFE is the presence of multiple equilibria. This paper shows that with (i) symmetric producers, (ii) perfectly inelastic demand, (iii) a price cap, and (iv) capacity constraints that bind with a positive probability, there exists a unique, symmetric SFE.