Breaking Barriers, Finding Boundaries: Not Obviously Manipulable Budget-Feasible Mechanism Design

Strategyproofness has been the holy grail in mechanism design for decades, providing strong incentive compatibility guarantees under the assumption of perfectly rational agents. However, this assumption is questionable when agents exhibit bounded rationality. Moreover, strategyproofness often imposes strong impossibility results that prevent mechanisms from surpassing certain approximation barriers. We study this tension in budget-feasible mechanism design, where a designer wants to procure services of maximum value from agents subject to a budget constraint. Here, strategyproofness imposes approximation barriers of $1+\sqrt{2}$ and $2$ for deterministic and randomized mechanisms, respectively. We investigate how much we can potentially gain under bounded rationality. We adopt the weaker notion of \emph{not obviously manipulable (NOM)}, which only prevents "obvious" strategic deviations. We fully resolve the achievable approximation guarantees under NOM: We derive a deterministic $2$-approximate NOM mechanism under the general class of monotone subadditive valuations. We also show that this bound is tight (even for additive valuations). Additionally, we provide a simple randomized $(1+\varepsilon)$-approximate NOM mechanism for any $\varepsilon > 0$. These results demonstrate a clear separation between strategyproof and NOM mechanisms. Our mechanisms use \emph{Golden Tickets} and \emph{Wooden Spoons} as natural design primitives, arising from our characterization of NOM mechanisms.