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Competitive dynamics on complex networks.

Jiuhua Zhao¹, Qipeng Liu¹, Xiaofan Wang¹

¹Department of Automation, Shanghai Jiao Tong University, and Key Laboratory of System Control and Information Processing, Ministry of Education of China, Shanghai 200240, China.

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|July 29, 2014

Summary

This summary is machine-generated.

In network competition, agent states converge based on network structure, not initial conditions. The competitor with higher Katz Centrality or PageRank typically wins, highlighting network influence on outcomes.

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Area of Science:

Complex Systems
Network Science
Game Theory

Background:

Dynamical network models are crucial for understanding emergent behaviors in systems with interacting agents.
Competition dynamics within networks are often influenced by agent states and network topology.
Predicting competition outcomes requires understanding how individual agent states aggregate and influence collective behavior.

Purpose of the Study:

To investigate how network structure and agent positions determine competition outcomes in a distributed consensus model.
To develop a method for predicting which competitor will achieve dominance based on network influence.
To compare the efficacy of a novel Influence Matrix (IM) with existing node centrality measures for predicting competition winners.

Main Methods:

Developed a dynamical network model with two competitors and normal agents using a distributed consensus protocol.
Computed an Influence Matrix (IM) to quantify the influence of each agent on others within the network.
Compared the predictive power of the IM against seven established node centrality measures (Katz Centrality, PageRank, etc.).

Main Results:

Agent states converge to a steady value determined by a convex combination of competitors' states, independent of initial conditions.
The Influence Matrix effectively predicts agent bias and identifies the likely competition winner.
Higher Katz Centrality in undirected networks and higher PageRank in directed networks correlate with a higher probability of winning.

Conclusions:

Network structure and competitor positioning are critical determinants of competition outcomes.
The Influence Matrix provides a robust tool for analyzing and predicting competition dynamics.
Node centrality measures, specifically Katz Centrality and PageRank, are valuable indicators of competitive success in networks.