We explore the approximation power of deterministic obviously strategy-proof mechanisms in auctions, where the objective is welfare maximization. A trivial ascending auction on the grand bundle guarantees an approximation of $\min\{m,n\}$ for all valuation classes, where $m$ is the number of items and $n$ is the number of bidders. We focus on two classes of valuations considered "simple": additive valuations and unit-demand valuations. For additive valuations, Bade and Gonczarowski [EC'17] have shown that exact welfare maximization is impossible. No impossibilities are known for unit-demand valuations. We show that if bidders' valuations are additive or unit-demand, then no obviously strategy-proof mechanism gives an approximation better than $\min\{m,n\}$. Thus, the aforementioned trivial ascending auction on the grand bundle is the optimal obviously strategy-proof mechanism. These results illustrate a stark separation between the power of dominant-strategy and obviously strategy-proof mechanisms. The reason for it is that for both of these classes the dominant-strategy VCG mechanism does not only optimize the welfare exactly, but is also "easy" both from a computation and communication perspective. In addition, we prove tight impossibilities for unknown single-minded bidders in a multi-unit auction and in a combinatorial auction. We show that in these environments as well, a trivial ascending auction on the grand bundle is optimal.

翻译：我们研究了确定性显然防策略性机制在拍卖中的近似能力，其中目标为福利最大化。针对所有估值类别，对大捆绑商品进行的平凡升价拍卖保证了$\min\{m,n\}$的近似比，其中$m$为商品数量，$n$为竞拍者数量。我们聚焦于两类被视为“简单”的估值：可加估值和单位需求估值。对于可加估值，Bade和Gonczarowski [EC'17]已证明精确福利最大化是不可能的。而对于单位需求估值，此前尚无已知的不可能性结果。我们证明：当竞拍者估值为可加或单位需求时，任何显然防策略性机制都无法实现优于$\min\{m,n\}$的近似比。因此，前述对大捆绑商品的平凡升价拍卖即为最优的显然防策略性机制。这些结果揭示了占优策略机制与显然防策略性机制之间存在显著的能力差距。其原因在于：对于这两类估值，占优策略的VCG机制不仅精确优化了福利，且在计算与通信层面均具有“简易”特性。此外，我们还针对多单位拍卖和组合拍卖中未知的单维竞拍者场景证明了紧的不可能性。我们表明在这些环境中，对大捆绑商品的平凡升价拍卖同样是最优的。