  In markets such as digital advertising auctions, bidders want to maximize
value rather than payoff. This is different to the utility functions typically
assumed in auction theory and leads to different strategies and outcomes. We
refer to bidders who maximize value as value bidders. While simple
single-object auction formats are truthful, standard multi-object auction
formats allow for manipulation. It is straightforward to show that there cannot
be a truthful and revenue-maximizing deterministic auction mechanism with value
bidders and general valuations. Approximation has been used as a means to
achieve truthfulness, and we study which approximation ratios we can get from
truthful approximation mechanisms. We show that the approximation ratio that
can be achieved with a deterministic and truthful approximation mechanism with
$n$ bidders and $m$ items cannot be higher than 1/n for general valuations. For
randomized approximation mechanisms there is a framework with a ratio of
O(sqrt(m)). We provide better ratios for environments with restricted
valuations.
