Scientists Model How Interactions Between Societies Can Trigger Chaotic Behaviour
Scientists at HSE MIEM have proposed a mathematical model explaining how interactions between societies can influence their stability. Based on the classical theory of evolutionary games, the study reveals an unexpected effect: even a weak informational influence of one society on another can cause one society to remain stable while the other exhibits chaotic behaviour among its individual members. The study has been published in the International Journal of Bifurcation and Chaos.
People rarely make decisions independently. Their choices are shaped by friends, colleagues, the news, the media, social networks, public rankings, opinion polls, and online discussions. To understand how these influences affect collective behaviour, researchers use mathematical models that enable them to explore possible scenarios for the evolution of social systems.
Researchers at HSE MIEM examined two hypothetical societies and modelled how their members interact using the Nowak–May spatial game, a variant of the Prisoner's Dilemma. In this model, agents occupy the nodes of a square grid and, at each step, choose a strategy—either cooperation for mutual benefit or defection for individual gain. After each round, agents compare their results and update their strategies by imitating the highest-scoring neighbour.
In the classic Nowak–May game, agents respond only to their nearest neighbours. The authors extended this approach by allowing agents to take into account the average state of either their own society or the other society. This enabled the researchers to simulate situations in which people's decisions are influenced not only by their direct interactions but also by the broader informational environment.
To assess the system's behaviour, the researchers analysed a stability indicator: the number of agents who never changed their strategy after the initial stage. The higher this indicator, the more stable the society's behaviour.
The results demonstrate that information exchange between two societies can affect them in different ways: one society remains stable, while in the other, agents randomly change their strategies.
However, chaos does not emerge across the entire society at once: the average proportion of cooperators may remain stable, but this does not necessarily indicate stability among all agents in the system. Individual agents may continue to change their strategies constantly. Abrupt shifts in a system’s behaviour do not always require strong external influences. In some cases, even a weak connection between societies can be enough for one of them to remain stable on the surface, while the other transitions to a less predictable regime.
Lev Shchur
'Such a transition does not result from random external influences: the model is deterministic, meaning that under the same initial conditions, it evolves according to the same rules. However, even a small difference in the parameters of the two societies—for example, in the benefits associated with the defection strategy—can dramatically alter the stability of the system,' explains Prof. Lev Shchur, Head of the Laboratory for Computational Physics at HSE MIEM.
According to the authors, the proposed approach can be used to study the spread of public sentiment, the impact of information, social conflicts, and processes occurring in digital media.
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