# Distributed Mechanism Design for Network Resource Allocation Problems

## TL;DR

This paper introduces a new framework called Distributed Mechanism Design, enabling decentralized network resource allocation where agents communicate locally, reducing overhead while achieving optimality in Nash equilibria.

## Contribution

It proposes two distributed mechanisms for network utility maximization that operate with local messages and fully implement optimal allocations at Nash equilibria.

## Key findings

- Mechanisms achieve optimal rate allocation in Nash equilibrium.
- Message space scales linearly with the number of agents.
- Applicable to unicast and multirate multicast protocols.

## Abstract

In the standard Mechanism Design framework, agents' messages are gathered at a central point and allocation/tax functions are calculated in a centralized manner, i.e., as functions of all network agents' messages. This requirement may cause communication and computation overhead and necessitates the design of mechanisms that alleviate this bottleneck. We consider a scenario where message transmission can only be performed locally so that the mechanism allocation/tax functions can be calculated in a decentralized manner. Each agent transmits messages to her local neighborhood, as defined by a given message-exchange network, and her allocation/tax functions are only functions of the available neighborhood messages. This scenario gives rise to a novel research problem that we call "Distributed Mechanism Design". In this paper, we propose two distributed mechanisms for network utility maximization problems that involve private and public goods with competition and cooperation between agents. As a concrete example, we use the problems of rate allocation in networks with either unicast or multirate multicast transmission protocols. The proposed mechanism for each of the protocols fully implements the optimal allocation in Nash equilibria and its message space dimensionality scales linearly with respect to the number of agents in the network.