Knightian Auctions

TL;DR

This paper explores auction mechanisms where players have limited valuation knowledge, revealing that dominant strategies perform poorly while undominated strategies can approximate optimal social welfare.

Contribution

It introduces bounds for social welfare in auctions with limited valuation knowledge, highlighting the differences between dominant and undominated strategies.

Findings

Dominant-strategy mechanisms cannot significantly improve social welfare.

Tight bounds are established for undominated strategies' social welfare.

Results apply to both deterministic and probabilistic strategies.

Abstract

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.