1. A system for supporting asset exchanges between parties of an auction including sellers and bidders, the system comprising: a transformation module configured to transform representations of bidders' auction bids into representations of bidders' bidding assets and representations of bidders' bid-on auction assets; a translation module configured to (i) translate representations of sellers' auction assets into vertices of a directed graph and representations of sellers' auction desires into edges of the directed graph and (ii) translate the representations of bidders' bidding assets into vertices of the directed graph and the representations of bidders' bid-on auction assets into edges of the directed graph; a cycle determination module configured to determine cycles in the directed graph, a cycle being a path starting at a given vertex and ending at the given vertex, the path including multiple edges and at least one intermediate vertex; and an offer module configured to transform the cycles into offers among the parties and to perform an action based on the offers.