Network Formation Games with Heterogeneous Players and the Internet Structure

TL;DR

This paper models the Internet's AS interconnection as a game with heterogeneous players, analyzing its static and dynamic properties, including equilibrium structures, convergence, and the impact of utility transfers.

Contribution

It introduces a game-theoretic framework for heterogeneous AS players, providing explicit analysis of topology properties, convergence rates, and the effects of utility transfers.

Findings

Explicit characterization of equilibrium topologies

Linear convergence rate under realistic dynamics

Limited feasible equilibria with utility transfers

Abstract

We study the structure and evolution of the Internet's Autonomous System (AS) interconnection topology as a game with heterogeneous players. In this network formation game, the utility of a player depends on the network structure, e.g., the distances between nodes and the cost of links. We analyze static properties of the game, such as the prices of anarchy and stability and provide explicit results concerning the generated topologies. Furthermore, we discuss dynamic aspects, demonstrating linear convergence rate and showing that only a restricted subset of equilibria is feasible under realistic dynamics. We also consider the case where utility (or monetary) transfers are allowed between the players.