Order of Play in Sequential Network Formation

Research in anthropology and neuroscience has shown that people have a cognitive limit on the number of stable relationships they can maintain. In this spirit, we consider a network formation game in which the cost of link formation is increasing in the agent's degree. In this class of games, as opposed to commonly studied games with a fixed cost of link formation, the order in which agents form the network (order of play) determines its final structure. In particular, we find that only certain orders of play can explain the formation of circle and complete bipartite networks. We also find that there is multiplicity of equilibria only when marginal costs of link formation are intermediate. Our results show as well that some orders of play are better than others for predicting the equilibrium structure when it is not unique, and that playing last is usually harmful.