On the Hardness of Truthful Online Auctions with Multidimensional Constraints

Abstract

This paper assess the prospect of creating truthful mechanisms for sponsored search auctions where advertisers have budget and time constraints. While the existing impossibility in this area by [4] addresses the situation where advertisers have budget limitations and static prices but not time limitations; our result applies to the common setting in practice where advertisers have time and budget limitations, prices are dynamic and advertisers act strategically on their time limitation as well as their budget.

We show that in cases where advertisers’ arrival and departure times are private information, no truthful deterministic mechanism for budgeted sponsored search with time constrained advertisers can perform well with respect to social welfare maximization. Essentially, to protect itself from advertisers’ time manipulation a truthful mechanism must give up significant social welfare.

It is also shown that even in cases where advertisers’ arrival and departure times are known to the mechanism, the existence of advertiser budgets is itself a problem. In this case a budgeted sponsored search mechanism with time constrained advertisers can not achieve non-trivial welfare approximation when using a local pricing scheme (a player pricing history is not taken into account). Also, it is shown that for a dynamic global pricing scheme no such truthful mechanism exists.