Complexity of Mechanism Design

TL;DR

This paper explores the complexity of designing truthful mechanisms in multiagent systems, showing NP-completeness for deterministic cases and tractability for randomized mechanisms, thus enabling practical solutions.

Contribution

It introduces an automated approach to mechanism design, demonstrating that randomized mechanisms can overcome computational hardness in preference aggregation.

Findings

Deterministic mechanism design is NP-complete without side payments.

Randomized mechanisms make the design problem computationally tractable.

Randomization can improve social outcomes in mechanism design.

Abstract

The aggregation of conflicting preferences is a central problem in multiagent systems. The key difficulty is that the agents may report their preferences insincerely. Mechanism design is the art of designing the rules of the game so that the agents are motivated to report their preferences truthfully and a (socially) desirable outcome is chosen. We propose an approach where a mechanism is automatically created for the preference aggregation setting at hand. This has several advantages, but the downside is that the mechanism design optimization problem needs to be solved anew each time. Focusing on settings where side payments are not possible, we show that the mechanism design problem is NP-complete for deterministic mechanisms. This holds both for dominant-strategy implementation and for Bayes-Nash implementation. We then show that if we allow randomized mechanisms, the mechanism design problem becomes tractable. In other words, the coordinator can tackle the computational complexity introduced by its uncertainty about the agents preferences BY making the agents face additional uncertainty.This comes at no loss, AND IN SOME cases at a gain, IN the(social) objective.