Distributed Mechanism Design with Learning Guarantees

TL;DR

This paper introduces distributed mechanisms for resource allocation among strategic agents that guarantee convergence to social welfare optimality and stability across various learning dynamics, even with local communication constraints.

Contribution

It proposes novel distributed mechanisms for resource sharing that ensure a unique Nash equilibrium, budget balance, and convergence guarantees under diverse learning dynamics.

Findings

Mechanisms produce a unique NE and implement social welfare maximization.

Guaranteed convergence for all learning dynamics in the Adaptive Best-Response class.

Numerical studies confirm convergence behavior across different graphs and dynamics.

Abstract

Mechanism design for fully strategic agents commonly assumes broadcast nature of communication between agents of the system. Moreover, for mechanism design, the stability of Nash equilibrium (NE) is demonstrated by showing convergence of specific pre-designed learning dynamics, rather than for a class of learning dynamics. In this paper we consider two common resource allocation problems: sharing $ K $ infinitely divisible resources among strategic agents for their private consumption (private goods), and determining the level for an infinitely divisible public good with $ P $ features, that is shared between strategic agents. For both cases, we present a distributed mechanism for a set of agents who communicate through a given network. In a distributed mechanism, agents' messages are not broadcast to all other agents as in the standard mechanism design framework, but are exchanged only in the local neighborhood of each agent. The presented mechanisms produce a unique NE and fully implement the social welfare maximizing allocation. In addition, the mechanisms are budget-balanced at NE. It is also shown that the mechanisms induce a game with contractive best-response, leading to guaranteed convergence for all learning dynamics within the Adaptive Best-Response dynamics class, including dynamics such as Cournot best-response, $ k- $period best-response and Fictitious Play. We also present a numerically study of convergence under repeated play, for various communication graphs and learning dynamics.