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

2025-02-17

AI Summary

This paper investigates the fundamental trade-off between incentive compatibility and social welfare approximation under budget feasibility, particularly when agents may be boundedly rational. Method: It systematically characterizes the efficacy of non-obvious manipulability (NOM) under budget constraints—the first such analysis—introducing two novel mechanism paradigms: “golden-ticket” (BNOM) and “wooden-spoon” (WNOM) mechanisms. It establishes tight deterministic 2-approximation ratios for monotone subadditive valuations under NOM, provides complete necessary and sufficient conditions for BNOM/ WNOM, and constructs randomized BNOM mechanisms achieving expected approximation ratios arbitrarily close to the optimal value of 1. Contribution/Results: The work reveals, for the first time, the performance separation between dominant-strategy incentive-compatible (DSIC) and NOM mechanisms under budget feasibility. By unifying mechanism design, game theory, subadditive analysis, and randomized construction, it significantly enhances robustness and efficiency in practical deployment.

Technology Category

• Game Theory and Economic Paradigms: Mechanism Design
• Multiagent Systems: Mechanism Design
• Search and Optimization: Mixed Discrete/Continuous Search

Application Category

• Economics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems
• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Security and Privacy: Large-scale security measurements

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.

Problem

• Exploring NOM in budget-feasible mechanisms
• Comparing DSIC and NOM guarantees
• Characterizing BNOM and WNOM mechanisms

Innovation

• Non-obvious manipulability (NOM) introduced
• Golden Tickets and Wooden Spoons used
• Budget-feasible mechanisms with tight bounds