On Core-Selecting and Core-Competitive Mechanisms for Binary Single-Parameter Auctions

Our work concerns the class of core-selecting mechanisms, as introduced by Ausubel and Milgrom [3]. Such mechanisms have been known to possess good revenue guarantees and some of their variants have been used in practice especially for spectrum and other public sector auctions. Despite their popularity, it has also been demonstrated that these auctions are generally non-truthful. As a result, current research has focused either on identifying core-selecting mechanisms with minimal incentives to deviate from truth-telling, such as the family of Minimum-Revenue Core-Selecting (MRCS) rules, or on proposing truthful mechanisms whose revenue is competitive against core outcomes. Our results contribute to both of these directions. We start with studying the core polytope in more depth and provide new properties and insights, related to the effects of unilateral deviations from a given profile. We then utilize these properties in two ways. First, we propose a truthful mechanism that is O(log n)-competitive against the MRCS benchmark. Our result is the first deterministic core-competitive mechanism for binary single-parameter domains. Second, we study the existence of non-decreasing payment rules, meaning that the payment of each bidder is a non-decreasing function of her bid. This property has been advocated by the core-related literature but it has remained an open question if there exist MRCS non-decreasing mechanisms. We answer the question in the affirmative, by describing a subclass of rules with this property.