Cooperation dynamics in dynamical networks with history-based decisions

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.