In this paper we address the problem of (1) representing bids for combinatorial auctions and (2) employing those structures for "reasoning". We propose a graph-based language who's novelty lies (1) in the use of generalized network flows to represent the bids and (2) in the interpretation of winner determination as an adequate aggregation of individual preferences. We motivate the language both from representational and reasoning points of view and show how our language represents the same class of expressivity of bids more concisely compared to existing work.