The Effectiveness of Golden Tickets and Wooden Spoons for Budget-Feasible Mechanisms

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.