Strategic Basins of Attraction, the Path Dominance Core, and Network Formation Games
Frank H. Page Jr.
Indiana University, Bloomington - Department of Economics; London School of Economics & Political Science (LSE) - Systemic Risk Centre
Myrna H. Wooders
Vanderbilt University - College of Arts and Science - Department of Economics
October 4, 2007
CAEPR Working Paper No. 2007-020
Given the preferences of players and the rules governing network formation, what networks are likely to emerge and persist? And how do individuals and coalitions evaluate possible consequences of their actions in forming networks? To address these questions we introduce a model of network formation whose primitives consist of a feasible set of networks, player preferences, the rules of network formation, and a dominance relation on feasible networks. The rules of network formation may range from non-cooperative, where players may only act unilaterally, to cooperative, where coalitions of players may act in concert. The dominance relation over feasible networks incorporates not only player preferences and the rules of network formation but also assumptions concerning 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 defined on the feasible set of networks. 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 well known models and their rules of network formation, such as those of Jackson and Wolinsky (1996) and Jackson and van den Nouweland (2005).
Number of Pages in PDF File: 37
Keywords: basins of attraction, network formation games, stable sets, path dominance core, Nash networks
JEL Classification: A14, C71, C72
Date posted: October 4, 2007