Multi-agent Adaptive Mechanism Design

Computer Vision & MultiModal AI

Published: arXiv: 2512.21794v1

Authors

Qiushi Han David Simchi-Levi Renfei Tan Zishuo Zhao

Abstract

We study a sequential mechanism design problem in which a principal seeks to elicit truthful reports from multiple rational agents while starting with no prior knowledge of agents' beliefs. We introduce Distributionally Robust Adaptive Mechanism (DRAM), a general framework combining insights from both mechanism design and online learning to jointly address truthfulness and cost-optimality. Throughout the sequential game, the mechanism estimates agents' beliefs and iteratively updates a distributionally robust linear program with shrinking ambiguity sets to reduce payments while preserving truthfulness. Our mechanism guarantees truthful reporting with high probability while achieving $\tilde{O}(\sqrt{T})$ cumulative regret, and we establish a matching lower bound showing that no truthful adaptive mechanism can asymptotically do better. The framework generalizes to plug-in estimators, supporting structured priors and delayed feedback. To our knowledge, this is the first adaptive mechanism under general settings that maintains truthfulness and achieves optimal regret when incentive constraints are unknown and must be learned.

Paper Summary

Problem

The main problem addressed by this research paper is the challenge of designing mechanisms that achieve optimal outcomes in the presence of uncertain and private information. In mechanism design, a central principal aims to create rules and institutions that incentivize rational agents to behave truthfully, but often relies on unrealistic assumptions about the availability of information. The paper aims to address the limitations of current mechanisms by developing a new approach that balances robustness and learning.

Key Innovation

The key innovation of this paper is the development of a Distributionally Robust Adaptive Mechanism (DRAM), which combines insights from mechanism design and online learning to create a new framework for adaptive mechanism design. DRAM estimates agents' beliefs, iteratively updates a distributionally robust linear program with shrinking ambiguity sets, and preserves truthfulness while reducing payments. This framework is novel because it addresses the challenge of learning players' beliefs and achieving optimal regret in the presence of unknown and private information.

Practical Impact

The practical impact of this research is significant, as it provides a new framework for designing adaptive mechanisms that can learn and adapt to changing environments. This has applications in a wide range of fields, including auctions, online advertising, business contracts, and trading rules. By ensuring truthful behaviors with high probability and achieving optimal payment regret, DRAM can improve the efficiency and fairness of decision-making processes in these areas.

Analogy / Intuitive Explanation

The core idea of DRAM can be understood through an analogy with navigation in an unfamiliar city. Imagine you're trying to find the shortest route to a destination, but you don't know the city's layout or the traffic patterns. You can't rely on a single map or prediction, as it may be outdated or incorrect. Instead, you use a combination of exploration and adaptation, gradually learning the city's layout and adjusting your route accordingly. Similarly, DRAM uses a combination of estimation and adaptation to learn the agents' beliefs and adjust the mechanism's parameters to achieve optimal outcomes.

Paper Information

Categories:

cs.GT cs.AI cs.LG cs.MA econ.TH

Published Date:

arXiv ID:

2512.21794v1

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