# Congestion Games with Complementarities

## TL;DR

This paper investigates congestion games with resource dependencies modeled through CES-inspired utility functions, analyzing equilibrium existence and complexity for various aggregation functions including Lp norms.

## Contribution

It introduces a framework for congestion games with diverse aggregation functions and characterizes conditions for pure Nash equilibrium existence.

## Key findings

- Existence of pure Nash equilibria depends on aggregation function properties.
- Complexity results for computing equilibria vary with aggregation functions.
- Characterization of aggregation functions that guarantee equilibrium existence.

## Abstract

We study a model of selfish resource allocation that seeks to incorporate dependencies among resources as they exist in modern networked environments. Our model is inspired by utility functions with constant elasticity of substitution (CES) which is a well-studied model in economics. We consider congestion games with different aggregation functions. In particular, we study $L_p$ norms and analyze the existence and complexity of (approximate) pure Nash equilibria. Additionally, we give an almost tight characterization based on monotonicity properties to describe the set of aggregation functions that guarantee the existence of pure Nash equilibria.