Price-mediated trade with quantity signals: An axiomatic approach

We consider a mechanism in which individuals send signals, indicating how much of each commodity they are willing to put up for trade. The mechanism produces prices and redistributes the commodities. We require that the map from signals to trades and prices, satisfy certain axioms and show that there are in essence only a finite number of mechanisms (i.e. maps) which satisfy these axioms. They include the Shapley mechanism and the Shapley-Shubik mechanism, and variants that lie "in between" the two. We also point out an open problem regarding a convexity property of these mechanisms, which is germane to the analysis of games based on them.