The Effectiveness of Golden Tickets and Wooden Spoons for Budget-Feasible Mechanisms
Bart de Keijzer, Guido Schäfer, Artem Tsikiridis, Carmine Ventre
TL;DR
This work studies budget-feasible mechanism design under non-obvious manipulability (NOM), introducing BNOM and WNOM as two extensions of truthfulness under bounded rationality. It develops the WillyWonka framework, using Golden Tickets and Wooden Spoons to achieve BNOM and WNOM, and builds a deterministic NOM mechanism that attains a $2$-approximation for monotone subadditive valuations, with a matching BNOM lower bound and a phi ($\varphi$) lower bound for WNOM. The paper then presents a full NOM characterization for BNOM and WNOM, including threshold-based conditions, and proves tight impossibility results for deterministic NOM under additive valuations. It further shows that randomized NOM mechanisms can overcome deterministic barriers, achieving a near-optimal $\gamma+\varepsilon$-approximation in expectation for monotone subadditive valuations, thereby highlighting the substantial gains from randomization in the NOM budget-feasible setting. Altogether, the results establish a clear separation between DSIC and NOM, provide a versatile mechanism-design template, and demonstrate practical strategies for incentive-compatible procurement under bounded rationality.
Abstract
One of the main challenges in mechanism design is to carefully engineer incentives ensuring truthfulness while maintaining strong social welfare approximation guarantees. But these objectives are often in conflict, making it impossible to design effective mechanisms. An important class of mechanism design problems that belong to this category are budget-feasible mechanisms. Here, the designer needs to procure services of maximum value from a set of agents while being on a budget, i.e., having a limited budget to enforce truthfulness. However, as empirical studies suggest, factors like limited information and bounded rationality question the idealized assumption that the agents behave perfectly rationally. Motivated by this, Troyan and Morill in 2022 introduced non-obvious manipulability (NOM) as a more lenient incentive compatibility notion. In this paper, we investigate whether resorting to NOM enables us to derive improved mechanisms in budget-feasible domains. We establish a tight bound of 2 on the approximation guarantee of budget-feasible mechanisms satisfying NOM for the general class of monotone subadditive valuation functions. Our result thus establishes a clear separation between the achievable guarantees for DSIC (perfectly rational agents) and NOM (imperfectly rational agents) as no truthful mechanism can achieve a guarantee better than 2.41. Along the way, we fully characterize BNOM and WNOM (which together form NOM) and derive matching upper and lower bounds, respectively. Conceptually, our characterization results suggest "Golden Tickets" and "Wooden Spoons" as natural means to realize BNOM and WNOM, respectively. Additionally, we show that randomized budget-feasible mechanisms satisfying BNOM can achieve an expected approximation ratio arbitrarily close to 1.