Online ascending auctions for gradually expiring items

We consider dynamic auction mechanisms for the allocation of multiple items. Items are identical, but have different expiration times, and each item must be allocated before it expires. Buyers are of dynamic nature, and arrive and depart over time. We are interested in situations where players act strategically and may mis-report their private parameters. Our goal is to design mechanisms that maximize the social welfare. We obtain three results. First, we design two detail-free auction mechanisms and prove that an approximatly optimal allocation is obtained for a large class of “semi-myopic ” selfish behavior of the players. Second, we provide a game-theoretic rational justification for acting in such a semi-myopic way. We suggest a notion of “Set-Nash ” equilibria, where we cannot pin-point a single best-response strategy, but rather only a set of possible best-response strategies. We show that, in our setting, these strategies are all semi-myopic, hence our auctions perform well on any combination of these. Third, to further justify the shift to this new notion, we prove that no ex-post implementation can obtain a constant fraction of the optimum