1. In a computer system, having one or more processors or virtual machines, one or more memory units, one or more input devices and one or more output devices, optionally a network, and optionally shared memory supporting communication among the processors, a computer implemented method for automatically finding the best matches between buyers' requests and sellers' offerings in a market of products or services, wherein such products or services are described by a plurality of arbitrary attributes, and for representing those matches in computer memory, and for communicating those matches, and for executing commitments based on those matches, said method comprising a microprocessor or virtual machine: (a) creating a buyers abstract representation of a plurality of intrinsic or extrinsic attributes of a request, and the relationship between at least one utility of the request and at least one state of the plurality of attributes; (b) creating a sellers abstract representation of a plurality of intrinsic or extrinsic attributes of an offer, and the relationship between the total price of the offering and at least one state of the plurality of attributes; (c) computing a rating for overall buyer's satisfaction of the plurality of attributes of a request with respect to a given offer; (d) determining the quantity and identity of assignments of sellers' offerings to buyers' requests, within the constraints of each party's stated extrinsic attributes, that produces the best set of matches for a given market; (e) capturing market data from market transactions and using the market data to automatically predict costs of attribute states in hypothetical transactions by steps comprising: (i) recording the request and offer data, along with the transaction price and quantity, for the committed transactions, and for other transactions that scored sufficiently well, and for requests and offers that were not matched in the market; (ii) inferring market value relationships from other data sources, such as sellers' advertisements, and or buyers' requests for proposals: (iii) using of mathematical function approximation techniques for constructing market value functions that describe the relationship between price and the states of various intrinsic or extrinsic attributes in a hypothetical market; (f) automatically joining buyers' requests in a consortium by steps comprising: (i) forming the best partition of the buyers' requests into groups or singletons of requests whose representation of attributes can be satisfied by the same seller offering: (ii) forming the combined abstract representation of the requests for the consortium, said representation which will satisfy each buyer in the consortium; (iii) constructing an artificial negotiating entity that will represent at least one consortium, and can conceal the identities of the buyers in the consortium; and (g) optionally signaling that the quantities and identities of assignments are accepted and that the transaction is committed by buyers and sellers.