Single-Parameter Domains and Implementation in Undominated Strategies

This paper studies Algorithmic Mechanism Design where the bidders are “single-parameter”(have the same private value for all desired outcomes), with a focus on Combinatorial Auctions(CA). We study four variants of the CA model: where each player desires a single bundle(“single-minded”) or he desires any one of several bundles (“multi-minded”), and where thedesired bundles are public information (“known”) or private information (“unknown”). Weprovide several mechanisms and examples in these settings. Our first main result is a generaltechnique to convert any algorithm to a truthful ascending mechanism for “known” domains (notonly for CA). For the “known” single-minded CA domain, it almost preserves the approximationratio of the original algorithm. Our second main result provides the first computationallyefficient mechanism for the case of “unknown” single-parameter multi-minded bidders, withclose to optimal welfare approximation. This mechanism also works in general, non single-parameter, combinatorial auctions, with some additional approximation loss. This mechanismis a computationally feasible implementation in undominated strategies, a notion that we defineand justify, and which we believe is of independent interest.