In a recent paper, we analyzed the self-assembly of a complex cooperation network. The network was shown to approach a state where every agent invests the same amount of resources. Nevertheless, highly-connected agents arise that extract extraordinarily high payoffs while contributing comparably little to any of their cooperations. Here, we investigate a variant of the model, in which highly-connected agents have access to additional resources. We study analytically and numerically whether these resources are invested in existing collaborations, leading to a fairer load distribution, or in establishing new collaborations, leading to an even less fair distribution of loads and payoffs.
Figure 1: Self-organized network evolved in the adaptive model. Nodes represent agents, while each link represents a non-vanishing cooperative interaction. The small dash on the link is a fairness indicator: the further it is shifted toward one agent, the lower is the fraction of the total investment into the cooperation that he contributes. Nodes extracting more payoff are shown in darker color and are placed toward the center of the community. The size of a node indicates the total investment the agent makes. In the final configuration all links within a BCC receive the same total investment and all nodes of the same degree make the same total investment.