Aiding the resilience of cooperation through the use of network rankings

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.