# Optimal Nash Equilibria for Bandwidth Allocation

## TL;DR

This paper introduces a nonlinear trading post mechanism for bandwidth allocation, demonstrating that most Nash equilibria are optimal across various welfare functions, and explores the limits of strategyproofness.

## Contribution

It presents a novel nonlinear variant of the trading post mechanism that achieves optimal Nash equilibria for a wide class of welfare functions, expanding the mechanism's effectiveness.

## Key findings

- Nash equilibria are optimal for almost all CES welfare functions.
- Strategyproof mechanisms are generally impossible, except for maxmin welfare.
- Small nonlinear modifications significantly enhance market mechanism power.

## Abstract

In bandwidth allocation, competing agents wish to transmit data along paths of links in a network, and each agent's utility is equal to the minimum bandwidth she receives among all links in her desired path. Recent market mechanisms for this problem have either focused on only Nash welfare, or ignored strategic behavior. We propose a nonlinear variant of the classic trading post mechanism, and show that for almost the entire family of CES welfare functions (which includes maxmin welfare, Nash welfare, and utilitarian welfare), every Nash equilibrium of our mechanism is optimal. We also prove that fully strategyproof mechanisms for this problem are impossible in general, with the exception of maxmin welfare. More broadly, our work shows that even small modifications (such as allowing nonlinear constraints) can dramatically increase the power of market mechanisms like trading post.