Evolutionary Dynamics in Complex Networks of Competing Boolean Agents

TL;DR

This paper explores how the structure of different complex networks influences the dynamics of competing Boolean agents, revealing that network topology critically affects stability, chaos, and system performance, with near-critical networks achieving optimal coordination.

Contribution

It demonstrates that network structure determines the dynamics and phase behavior of Boolean agent systems, and shows that evolution drives near-critical networks to optimal coordination.

Findings

GDNets exhibit very stable dynamics across all connection numbers.

Kauffman's NK networks become chaotic when K > 2.

Near-critical GDRNets evolve to high coordination and near-optimal performance.

Abstract

We investigate the dynamics of network minority games on Kauffman's NK networks (Kauffman nets), growing directed networks (GDNets), as well as growing directed networks with a small fraction of link reversals (GDRNets). We show that the dynamics and the associated phase structure of the game depend crucially on the structure of the underlying network. The dynamics on GDNets is very stable for all values of the connection number $K$, in contrast to the dynamics on Kauffman's NK networks, which becomes chaotic when $K>K_c=2$. The dynamics of GDRNets, on the other hand, is near critical. Under a simple evolutionary scheme, the network system with a "near" critical dynamics evolves to a high level of global coordination among its agents. In particular, the performance of the system is close to the optimum for the GDRNets; this suggests that criticality leads to the best performance. For Kauffman nets with $K>3$, the evolutionary scheme has no effect on the dynamics (it remains chaotic) and the performance of the MG resembles that of a random choice game (RCG).