Contractually stable networks

Abstract

We develop a theoretical framework that allows us to study which bilateral links and coalition structures are going to emerge at equilibrium. We define the notion of coalitional network to represent a network and a coalition structure, where the network speciÖes the nature of the relationship each individual has with his coalition members and with individuals outside his coalition. To predict the coalitional networks that are going to emerge at equilibrium we propose the concept of contractual stability which requires that any change made to the coalitional network needs the consent of both the deviating players and their original coalition partners. We show that there always exists a contractually stable coalitional network under the simple majority decision rule and the component-wise egalitarian or majoritarian allocation rules. Moreover, requiring the consent of group members may help to reconcile stability and e¢ ciency

Structural Holes in Social Networks with Exogenous Cliques

“…By deleting the link jk, agent j obtains ∆Π j = c −c(t). Specifically,c(t) = 3t−1 12 when the deletion of the link jk creates two new essential agents, i and h. If this deviation creates additional essential agents because of the structure of the M j -group, thenc(t) > 3t−1 12 . In any case, the deviation is profitable whenever c >c(t).…”

Tractable and Consistent Random Graph Models

“…36 If the error term has an atomless distribution, then the strictness is inconsequential. Let F (•) be the distribution of 33 For additional theoretical underpinnings of coalition-based network formation models see Jackson and van den Nouweland (2005); Caulier et al (2013). 34 For instance if X(g ) were a list of the individuals' ages, then it might be that i's benefit from the subgraph is a function of i's distance from the average characteristics:…”

Stable and efficient coalitional networks

“…Two di¤erent decision rules for consent are analyzed: simple majority and unanimity. 6 Looking at two models of coalitional network formation (a connections model with cost sharing among municipalities and a R&D model where …rms form R&D bilateral agreements and belong to alliances), we observe that requiring the consent of coalition members under the simple majority or unanimity decision rule may help to reconcile stability and e¢ ciency. 7 We also show that this new framework provides us results that one cannot obtain if coalition formation and network formation are tackled separately and independently.…”

“…See Smith (2005). 6 All individuals who are part of a criminal organization like the Hells Angels are sponsored by an o¢ cial member and have to gain the approval of 100 percent of members in order to climb the hierarchy. See Morselli (2009).…”