Strategic basins of attraction, the path dominance core, and network formation games

We introduce a model of network formation whose primitives consist of a feasible set of networks, player preferences, rules of network formation, and a dominance relation on feasible networks. Rules may range from noncooperative, where players may only act unilaterally, to cooperative, where coalitions of players may act in concert. The dominance relation over feasible networks incorporates player preferences, the rules of network formation, and the degree of farsightedness of players. A specification of the primitives induces an abstract game consisting of (i) a feasible set of networks, and (ii) a path dominance relation. Using this induced game we characterize sets of network outcomes that are likely to emerge and persist. Finally, we apply our approach and results to characterize the equilibrium of some well-known models and their rules of network formation, such as those of Jackson and Wolinsky, and Jackson and van den Nouweland.