In a symmetric Nash Equilibrium the prices of both goods are randomized in an atomless fashion for the most part of the parameter space apart from the case when the two goods are strongly substitutable in which case the less valuable good is not sold at all. Only when the goods are either independently valued or are substitutes is it feasible that the two prices are randomized independently. When the goods are complements and one of the goods is priced high the other can not be priced in the upper part of its support implying local negative correlation between the two prices. The stronger is the complementarity.
