Stability of subsystem solutions in agent-based models
Authored by Matjaz Perc
Date Published: 2018
DOI: 10.1088/1361-6404/aa903d
Sponsors:
Slovenian Research Agency
Platforms:
No platforms listed
Model Documentation:
Other Narrative
Mathematical description
Model Code URLs:
Model code not found
Abstract
The fact that relatively simple entities, such as particles or neurons,
or even ants or bees or humans, give rise to fascinatingly complex
behaviour when interacting in large numbers is the hallmark of complex
systems science. Agent-based models are frequently employed for
modelling and obtaining a predictive understanding of complex systems.
Since the sheer number of equations that describe the behaviour of an
entire agent-based model often makes it impossible to solve such models
exactly, Monte Carlo simulation methods must be used for the analysis.
However, unlike pairwise interactions among particles that typically
govern solid-state physics systems, interactions among agents that
describe systems in biology, sociology or the humanities often involve
group interactions, and they also involve a larger number of possible
states even for the most simplified description of reality. This begets
the question: when can we be certain that an observed simulation outcome
of an agent-based model is actually stable and valid in the large
system-size limit? The latter is key for the correct determination of
phase transitions between different stable solutions, and for the
understanding of the underlying microscopic processes that led to these
phase transitions. We show that a satisfactory answer can only be
obtained by means of a complete stability analysis of subsystem
solutions. A subsystem solution can be formed by any subset of all
possible agent states. The winner between two subsystem solutions can be
determined by the average moving direction of the invasion front that
separates them, yet it is crucial that the competing subsystem solutions
are characterised by a proper composition and spatiotemporal structure
before the competition starts. We use the spatial public goods game with
diverse tolerance as an example, but the approach has relevance for a
wide variety of agent-based models.
Tags
Complex networks
Evolution
Dynamics
statistical physics
Phase transition
systems
pattern formation
Monte Carlo method
Evolutionary games
Lessons
Phase-transitions
Public goods
game
Human cooperation