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

TL;DR

This paper explores budget-feasible mechanisms under non-obvious manipulability (NOM), establishing tight bounds on their approximation guarantees and introducing concepts like Golden Tickets and Wooden Spoons to realize NOM properties.

Contribution

It provides a tight bound of 2 for NOM-based mechanisms, characterizes BNOM and WNOM, and introduces natural mechanisms called Golden Tickets and Wooden Spoons.

Findings

Tight bound of 2 on approximation guarantee for NOM mechanisms.

Characterization of BNOM and WNOM and their bounds.

Randomized BNOM mechanisms can approach an approximation ratio of 1.

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.