Strongly Stable Networks

Abstract

We analyze the formation of networks among individuals. In particular, we examine the existence of networks that are stable against changes in links by any coalition of individuals. We show that to investigate the existence of such strongly stable networks one can restrict focus on a component-wise egalitarian allocation of value. We show that when such strongly stable networks exist they coincide with the set of e cient networks (those maximizing the total productive value). We show that the existence of strongly stable networks is equivalent to core existence in a derived cooperative game and use that result to characterize the class of value functions for which there exist strongly stable networks via a "top convexity" condition on the value function on networks. We also consider a variation on strong stability where players can make side payments, and examine situations where value functions may be non-anonymous -depending on player labels.

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

“…Until now, most of the economic literature on networks has focused on linking networks (see Jackson 2005 for an excellent survey). In an undirected (or linking) 8 In particular, we focus on the notion of directed networks introduced in Page, Wooders, and Kamat (2005).…”

“…Thus, for example, the initially deviating coalition S 1 will not be deterred from changing network G 0 to network G 1 even if network G 1 is not preferred to network G = G 0 , as long as the ultimate network outcome G = G h is preferred to G 0 , that is, as long as G 0 ≺ S 1 G h . 17 …”

“…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). …”

Network Economics and the Environment: Insights and Perspectives

“…The notion of Nash-pairwise stability, allowing both the coordinated objection of pairs of agents and the severance of any number of an agent's own connections, is instead a refinement of the Nash equilibrium. The even more demanding notion of strong stability (Jackson and van den Nouweland, 2005), assumes that any subset of agents can coordinate in the joint revision of their links, and possesses similar features to the strong Nash equilibrium of games in strategic form.…”

Collusive Networks in Market‐Sharing Agreements in the Presence of an Antitrust Authority

“…Prominent contributions to this literature include, among others, Jackson and Wolinsky (1996), Goyal (1993), Dutta and Mutuswami (1997) and Jackson and van den Nouweland (2005). In particular, in the …rst, the formation and stability of social networks are modeled when agents choose to maintain or destroy links using the notion of pairwise stability.…”