In a preferred embodiment, this invention includes software processes distributed on one or more computer systems that exchange messages in order to facilitate an intermediated exchange of financial commodities between a plurality of participants. The messages are exchanged according to a preferred protocol that leads to a satisfactory exchange that meets the objectives of the participants, and that substantially maximizes in a fair manner the total amount of financial commodities exchanged. Optionally, the invention employs heuristic rules in association with the preferred protocol that adapt the protocol to the time and exchange requirements of financial commodities. In other embodiments, this invention is equally applicable to the exchange of any tangible or intangible commodities. In a general embodiment, this invention further includes a preferred message-exchange protocol for the construction of computer programs representing exchange participants and an intermediary. These constructed computer programs exchange messages such that a satisfactory intermediated exchange of commodities is substantially certain to be achieved.