Inefficiency caused by random matching and heterogeneity

I study an economy with sellers and buyers with unit supplies and unit demands. Both parties have valuations uniformly distributed on a unit interval. I quantify the inefficiency, compared to the Walrasian markets, when the agents meet randomly. There are several causes of inefficiency that I deal with separately. First, even if there is perfect information about valuations it makes a difference whether all agents participate in the markets or whether only those who would trade in the Walrasian market participate. The same applies when there is private information about valuations.