In many aspects of life on earth, individuals may engage in cooperation with others to contribute towards a goal they may share, which can also ensure self-preservation. In evolutionary game theory, the act of cooperation can be considered as an altruistic act of an individual producing some form of benefit or commodity that can be utilised by others they are associated with, which comes at some personal cost. Under certain conditions, individuals make use of information that they are able to perceive within a group in order to aid with their choices for who they should associate themselves within these cooperative scenarios. However, cooperative individuals can be taken advantage of by opportunistic defectors, which can cause significant disruption to the population. We study a model where the decision to establish interactions with potential partners is based on the opportune integration of the individual’s private ability to perceive the intentions of others (private information) and the observation of the population, information that is available to every individual (public information). When public information is restricted to a potential partners current connection count, the population becomes highly cooperative but rather unstable with frequent invasions of cheaters and recoveries of cooperation. However, when public information considers the previous decisions of the individuals (accepted / rejected connections) the population is slightly less cooperative but more stable. Generally, we find that allowing the observation of previous decisions, as part of the available public information, can often lead to more stable but fragmented and less prosperous networks. Our results highlight that the ability to observe previous individual decisions, balanced by individuals personal information, represents an important aspect of the interplay between individual decision-making and the resilience of cooperation in structured populations.

Across various scenarios, individuals cooperate with others to contribute towards a shared goal and ensure self-preservation. In game theory, the act of cooperation is considered as an individual producing some form of benefit to be utilised by others, under the expectation others will return the favour. In several scenarios, individuals make use of their own information to aid with their decision about who to connect and cooperate with. However, the choice of cooperation can be taken advantage of by opportunistic defectors, which can lead to significant disruption. This paper investigates how the diversity of opinion can contribute to the structure and mechanics of a dynamical network model and to the resilience of cooperation, by utilising a computational model where individuals make use of both public and private information to implement their decision. Our results show that increasing diversity leads to more stable, less connected and less prosperous networks coupled to more frequent, but shallower information cascades. Our work generally shows that the outcome of the conflict between cooperators and cheaters strongly depends on the interplay between population structure, individual decision making and individual opinions.

The stability of communities - whether biological, social, economic, technological or ecological depends on the balance between cooperation and cheating. While cooperation strengthens communities, selfish individuals, or "cheaters," exploit collective benefits without contributing. If cheaters become too prevalent, they can trigger the collapse of cooperation and of the community, often in an abrupt manner. A key challenge is determining whether the risk of such a collapse can be detected in advance. To address this, we use a combination of evolutionary graph theory and machine learning to examine how one can predict the unravel of cooperation on complex networks. By introducing few cheaters into a structured population, we employ machine learning to detect and anticipate the spreading of cheaters and cooperation collapse. Using temporal and structural data, the presented results show that prediction accuracy improves with stronger selection strength and larger observation windows, with CNN-Seq-LSTM and Seq-LSTM best performing models. Moreover, the accuracy for the predictions depends crucially on the type of game played between cooperators and cheaters (i.e., accuracy improves when it is more advantageous to defect) and on the community structure. Overall, this work introduces a machine learning approach into detecting abrupt shifts in evolutionary graph theory and offer potential strategies for anticipating and preventing cooperation collapse in complex social networks.

In many aspects of life on earth, individuals may engage in cooperation with others to contribute towards a goal they may share, which can also ensure self-preservation. In evolutionary game theory, the act of cooperation can be modelled as an altruistic act of an individual producing some form of benefit that can be utilised by others they are associated with at some personal cost. In various scenarios, individuals make use of information that they can perceive within a group to aid with their decision-making regarding who they should associate and cooperate with. However, cooperative individuals can be taken advantage of by opportunistic defectors, which can cause significant disruption to the population. We study a model where the decision to establish interactions with potential partners is based on the opportune integration of the individual’s private ability to perceive the intentions of others (private information) and the network position (ranking) of potential partners (public information). We find that there are rankings, such as degree and eigenvector, which can lead to a significant increase to the prosperity of the network, but this greatly increases the likelihood of a network succumbing to cheater invasion. Other rankings, such as betweeness, can instead lead to more stable resilient networks whilst also cultivating some degree of payoff. Our results highlight how commonly used network rankings can be utilised to aid with connection formation within networks and in turn can be utilised to improve the well-being of these networks, helping with stability and allowing for individuals to cultivate cooperation amongst each other. Private information should also continue to be considered when examining the dynamics of these networks as it appears to be a primary driver of encouraging individual agency.