We study single-good auctions when each player knows his own valuation only within a constant multiplicative factor Δ e (0, 1), known to the mechanism designer. 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.
['Alessandro Chiesa', 'Silvio Micali', 'Zeyuan Allen Zhu']
Mechanism design with approximate valuations