# Network Investment Game with Wardrop Followers

## TL;DR

This paper models a two-stage network investment game involving providers investing in bandwidth and users selecting services to minimize processing time, analyzing equilibrium outcomes and the impact of competition.

## Contribution

It introduces a novel two-stage game model with Wardrop followers and provides reduction techniques for series-parallel graphs to analyze equilibria.

## Key findings

- Competition influences total user costs
- Series-parallel graphs can be simplified to single-edge games
- Equilibrium analysis reveals strategic investment and routing behaviors

## Abstract

We study a two-sided network investment game consisting of two sets of players, called providers and users. The game is set in two stages. In the first stage, providers aim to maximize their profit by investing in bandwidth of cloud computing services. The investments of the providers yield a set of usable services for the users. In the second stage, each user wants to process a task and therefore selects a bundle of services so as to minimize the total processing time. We assume the total processing time to be separable over the chosen services and the processing time of each service to depend on the utilization of the service and the installed bandwidth. We provide insights on how competition between providers affects the total costs of the users and show that every game on a series-parallel graph can be reduced to an equivalent single edge game when analyzing the set of subgame perfect Nash equilibria.