On the Power of Randomization for Obviously Strategy-Proof Mechanisms
Shiri Ron, Daniel Schoepflin
TL;DR
The paper investigates randomized obviously strategy-proof (OSP) mechanisms in canonical auction settings, revealing a clear separation between the power of randomized versus deterministic OSP. By employing universal OSP (a distribution over deterministic OSP protocols) and secretary-style sampling via generalized ascending auctions, it achieves constant-factor welfare approximations in multi-unit and combinatorial auctions across additive, unit-demand, and single-minded valuations, while also proving nontrivial lower bounds (e.g., no randomized OSP can beat $ rac{8}{7}$ in some cases and a $0.875$-approximation lower bound in general). The methodological backbone combines a Yao-style reduction to deterministic mechanisms with a structural “bad leaf–good leaf” lemma to bound welfare under OSP constraints, yielding both constructive upper bounds and impossibility results. These results illuminate a meaningful separation between randomized and deterministic OSP mechanisms and point to rich directions for future work on broader valuation classes and tighter constants.
Abstract
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.