Navigable Networks as Nash Equilibria of Navigation Games

TL;DR

This paper demonstrates that networks optimized for navigation efficiency and minimal cost are Nash equilibria of a game, sharing structural properties with real-world networks like the Internet and brain networks.

Contribution

It introduces a game-theoretic model showing that real networks resemble minimalistic Nash equilibrium structures optimized for navigation and cost.

Findings

Real networks contain skeletons similar to Nash equilibria of the proposed game.

Identifying these skeletons allows for targeted modifications to improve or disrupt navigation.

Networks are optimized structures balancing cost and navigability.

Abstract

The common sense suggests that networks are not random mazes of purposeless connections, but that these connections are organised so that networks can perform their functions well. One function common to many networks is targeted transport or navigation. Using game theory, here we show that minimalistic networks designed to maximise the navigation efficiency at minimal cost share basic structural properties with real networks. These idealistic networks are Nash equilibria of a network construction game whose purpose is to find an optimal trade-off between the network cost and navigability. We show that these skeletons are present in the Internet, metabolic, English word, US airport, Hungarian road networks, and in a structural network of the human brain. The knowledge of these skeletons allows one to identify the minimal number of edges by altering which one can efficiently improve or paralyse navigation in the network.