We investigate the problem of designing randomized obviously strategy-proof (OSP) mechanisms in several canonical auction settings. Obvious strategy-proofness, introduced by Li [American Economic Review, 2017], strengthens the well-known concept of dominant-strategy incentive compatibility (DSIC). Loosely speaking, it ensures that even agents who struggle with contingent reasoning can identify that their dominant strategy is optimal. Thus, one would hope to design OSP mechanisms with good approximation guarantees. Unfortunately, Ron [SODA,2024] has shown that deterministic OSP mechanisms fail to achieve an approximation better than $\min\{m,n\}$ where $m$ is the number of items and $n$ is the number of bidders, even for the simple settings of additive and unit-demand bidders. We circumvent these impossibilities by showing that randomized mechanisms that are obviously strategy-proof in the universal sense obtain a constant factor approximation for these classes. We show that this phenomenon occurs also for the setting of a multi-unit auction with single-minded bidders. Thus, our results provide a more positive outlook on the design of OSP mechanisms and exhibit a stark separation between the power of randomized and deterministic OSP mechanisms. To complement the picture, we provide impossibilities for randomized OSP mechanisms in each setting. While the deterministic VCG mechanism is well known to output an optimal allocation in dominant strategies, we show that even randomized OSP mechanisms cannot obtain more than $87.5\%$ of the optimal welfare. This further demonstrates that OSP mechanisms are significantly weaker than dominant-strategy mechanisms.

翻译：我们在若干经典拍卖场景中研究随机化显然策略证明（OSP）机制的设计问题。显然策略证明性由Li[《美国经济评论》,2017]提出，强化了广为人知的占优策略激励相容（DSIC）概念。粗略而言，它确保即使不擅长或然推理的参与者也能识别其占优策略的最优性。因此，人们期望设计具有良好近似保证的OSP机制。然而，Ron[SODA,2024]已证明确定性OSP机制即使对于简单的可加估值和单位需求竞拍者场景，也无法获得优于$\min\{m,n\}$的近似比，其中$m$为物品数量，$n$为竞拍者数量。我们通过证明在普适意义上具有显然策略证明性的随机化机制能为此类场景提供常数倍近似，从而规避了这些不可能性。我们进一步证明该现象同样出现在单需求竞拍者的多单位拍卖场景中。因此，我们的研究结果为OSP机制设计提供了更积极的展望，并揭示了随机化与确定性OSP机制在能力上的显著差异。为完善理论图景，我们在每个场景中补充了随机化OSP机制的不可能性结果。尽管确定性VCG机制在占优策略中输出最优分配已是共识，但我们证明即使随机化OSP机制也无法获得超过$87.5\%$的最优社会福利。这进一步表明OSP机制显著弱于占优策略机制。