# Algorithms for Nash and Pareto Equilibria for Resource Allocation in Multiple Femtocells

## TL;DR

This paper develops decentralized algorithms for resource allocation in multi-femtocell networks, achieving Nash and Pareto equilibria to ensure QoS and fairness with lower complexity.

## Contribution

It introduces novel decentralized algorithms for finding Nash, Pareto, and bargaining equilibria in multi-femtocell systems, improving efficiency and fairness.

## Key findings

- Algorithms successfully achieve QoS guarantees for users.
- Decentralized approach reduces computational complexity.
- Fair and Pareto-efficient equilibria are attainable.

## Abstract

We consider a cellular system with multiple Femtocells operating in a Macrocell. They are sharing a set of communication channels. Each Femtocell has multiple users requiring certain minimum rate guarantees. Each channel has a peak power constraint to limit interference to the Macro Base Station (BS). We formulate the problem of channel allocation and power control at the Femtocells as a noncooperative Game. We develop decentralized algorithms to obtain a Coarse Correlated equilibrium that satisfies the QoS of each user. If the QoS of all the users cannot be satisfied, then we obtain a fair equilibrium. Finally we also provide a decentralized algorithm to reach a Pareto and a Nash Bargaining solution which has a much lower complexity than the algorithm to compute the NE.