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We present an extensive breakdown of the auction design space that captures the essential similarities and differences of many auction mechanisms in a format more descriptive and useful than simple taxonomies. This parametrization serves as an organizational framework in which to classify work within the field and uncovers parameter combinations corresponding to novel mechanisms. The structured characterization of auction rules can be exploited for the modular design of configurable auction servers. It also facilitates the communication of auction rules to software agents, enabling the automation of flexible market-based negotiation. Journal of Economic Literature Classification Numbers: C70, D44.