Strong activity rules for iterative combinatorial auctions

Activity rules have emerged in recent years as an important aspect of practical auction design. The role of an activity rule in an iterative auction is to suppress strategic behavior by bidders and promote simple, continual, meaningful bidding and thus, price discovery. These rules find application in the design of iterative combinatorial auctions for real world scenarios, for example in spectrum auctions, in airline landing slot auctions, and in procurement auctions. We introduce the notion of strong activity rules, which allow simple, consistent bidding strategies while precluding all behaviors that cannot be rationalized in this way. We design such a rule for auctions with budget-constrained bidders, i.e., bidders with valuations for resources that are greater than their ability to pay. Such bidders are of practical importance in many market environments, and hindered from bidding in a simple and consistent way by the commonly used revealed-preference activity rule, which is too strong in such an environment. We consider issues of complexity, and provide two useful forms of information feedback to guide bidders in meeting strong activity rules. As a special case, we derive a strong activity rule for non-budget-constrained bidders. The ultimate choice of activity rule must depend, in part, on beliefs about the types of bidders likely to participate in an auction event because one cannot have a rule that is simultaneously strong for both budget-constrained bidders and quasi-linear bidders.