Non-Monetary Mechanism Design without Distributional Information: Using Scarce Audits Wisely

2025-02-12

AI Summary

This paper studies repeated resource allocation without monetary transfers and without prior knowledge of agents’ utility distributions, aiming to maximize social welfare under scarce and costly high-precision auditing. We propose an incentive-compatible mechanism combining flag-based signaling with dynamic future penalties, circumventing the traditional revelation principle via a novel auxiliary-game analytical framework. Our theoretical contributions include: (i) the first $T$-independent $O(K^2)$ regret bound on social welfare and an $O(K^3 log T)$ bound on expected audit cost; (ii) tight $Omega(K)$ and $Omega(1)$ lower bounds on welfare regret and audit cost, respectively; and (iii) guaranteed approximate Bayesian incentive compatibility. Methodologically, we integrate probabilistic calibration, counterfactual auditing policies, and responsive flag design—ensuring efficiency, implementability, and verifiability.

Technology Category

• Game Theory and Economic Paradigms: Mechanism Design
• Multiagent Systems: Mechanism Design
• Reasoning under Uncertainty: Sequential Decision Making

Application Category

• Economics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems
• Responsible Web: Machine-in-the-loop, human agency and autonomy
• Security and Privacy: Large-scale security measurements

Abstract

We study a repeated resource allocation problem with strategic agents where monetary transfers are disallowed and the central planner has no prior information on agents' utility distributions. In light of Arrow's impossibility theorem, acquiring information about agent preferences through some form of feedback is necessary. We assume that the central planner can request powerful but expensive audits on the winner in any round, revealing the true utility of the winner in that round. We design a mechanism achieving $T$-independent $O(K^2)$ regret in social welfare while requesting $O(K^3 log T)$ audits in expectation, where $K$ is the number of agents and $T$ is the number of rounds. We also show an $Omega(K)$ lower bound on the regret and an $Omega(1)$ lower bound on the number of audits when having low regret. Algorithmically, we show that incentive-compatibility can be mostly enforced with an accurate estimation of the winning probability of each agent under truthful reporting. To do so, we impose future punishments and introduce a *flagging* component, allowing agents to flag any biased estimate (we show that doing so aligns with individual incentives). On the technical side, without monetary transfers and distributional information, the central planner cannot ensure that truthful reporting is exactly an equilibrium. Instead, we characterize the equilibrium via a reduction to a simpler *auxiliary game*, in which agents cannot strategize until late in the $T$ rounds of the allocation problem. The tools developed therein may be of independent interest for other mechanism design problems in which the revelation principle cannot be readily applied.

Problem

• Non-monetary resource allocation with strategic agents
• Achieving low regret without distributional information
• Enforcing incentive-compatibility with limited audits

Innovation

• Non-monetary audits for utility revelation
• Flagging mechanism ensures truthful reporting
• Auxiliary game simplifies equilibrium characterization