Competitive Dynamics on Complex Networks

TL;DR

This paper models competitive dynamics on complex networks, showing how network structure influences which competitor wins, and introduces an Influence Matrix to predict outcomes based on node influence measures.

Contribution

It introduces an Influence Matrix to predict competition outcomes and compares its effectiveness with traditional centrality measures like Katz and PageRank.

Findings

Higher Katz Centrality correlates with winning in undirected networks.

Higher PageRank correlates with winning in directed networks.

Network structure significantly impacts competitive success.

Abstract

We consider a dynamical network model in which two competitors have fixed and different states, and each normal agent adjusts its state according to a distributed consensus protocol. The state of each normal agent converges to a steady value which is a convex combination of the competitors' states, and is independent of the initial states of agents. This implies that the competition result is fully determined by the network structure and positions of competitors in the network. We compute an Influence Matrix (IM) in which each element characterizing the influence of an agent on another agent in the network. We use the IM to predict the bias of each normal agent and thus predict which competitor will win. Furthermore, we compare the IM criterion with seven node centrality measures to predict the winner. We find that the competitor with higher Katz Centrality in an undirected network or higher PageRank in a directed network is much more likely to be the winner. These findings may shed new light on the role of network structure in competition and to what extent could competitors adjust network structure so as to win the competition.