Rouwendal, J. (1990). Existence and uniqueness of stochastic price equilibria in heterogeneous markets Regional Science and Urban Economics, 20(1):43--64.

This paper contributes to the literature on existence and uniqueness of stochastic market equilibria in two ways. First it is pointed out that gross substitutability is a fairly general characteristic of the (expected) market demand functions that result when choice behaviour of individual actors is described by means of discrete choice models. This enables one to reach simpler proofs of existence and uniqueness of price equilibria. Second, a necessary and sufficient condition for uniqueness is formulated. This is shown for a model in which, as a further improvement, the unrealistic assumption of balance is dropped. The special case of a balanced market is later on discussed separately and similar results are shown to hold there.