An analysis of constructive network formation models

We study a family of network formation models to determine how payment rules affect the final network topologies that emerge. In our model a set of nodes starts out without any edges and the nodes must pay for the creation of edges using one of several different payment mechanisms. Example payment mechanisms include one node paying for the whole edge, and the cost being shared equally between the two nodes. We show how the set of networks formed by some payment rules are subsets of those formed by other rules. We also perform extensive empirical tests on networks of up to 10 nodes. These tests reveal some interesting patterns in the connectivity, stability, and fairness of the networks generated by the various payment rules given a fixed link cost.