  We study single-good auctions in a setting where each player knows his own
valuation only within a constant multiplicative factor \delta{} in (0,1), and
the mechanism designer knows \delta. The classical notions of implementation in
dominant strategies and implementation in undominated strategies are naturally
extended to this setting, but their power is vastly different.
  On the negative side, we prove that no dominant-strategy mechanism can
guarantee social welfare that is significantly better than that achievable by
assigning the good to a random player.
  On the positive side, we provide tight upper and lower bounds for the
fraction of the maximum social welfare achievable in undominated strategies,
whether deterministically or probabilistically.
