Social Capital and Conventions: A Social Networks Perspective

We introduce a spatial cost topology in thenetwork formation model analyzed by Jackson andWolinsky, Journal of Economic Theory 71 (1996), 44--74. This cost topology mightrepresent geographical, social, or individualdifferences. It describes variable costs ofestablishing social network connections.Participants form links based on a cost-benefitanalysis. We examine the pairwise stable networkswithin this spatial environment. Incentives varyenough to show a rich pattern of emergingbehavior. We also investigate the subgame perfectimplementation of pairwise stable and efficientnetworks. We construct a multistage extensiveform game that describes the formation of linksin our spatial environment. Finally, we identifythe conditions under which the subgame perfectNash equilibria of these network formation gamesare stable. We analyze the dynamic implications of learningin a large population coordination game where boththe actions of the players and the communicationnetwork evolve over time. Cost considerations ofsocial interaction are incorporated by consideringa circular model with endogenous neighborhoods,meaning that the locations of the players arefixed but players can create their owncommunication network.The dynamic processdescribing medium-run behavior is shown toconverge to an absorbing state, which may becharacterized by coexistence of conventions.In the long run, when mistake probabilitiesare small but nonvanishing, coexistence ofconventions is no longer sustainable as therisk-dominant convention becomes the uniquestochastically stable state. We create and investigate a system that iscapable of observing the accumulation of socialcapital and the effect of social capital accumulationon behavior of individually rational players. In the firstmodel, we develop a restricted system to showthat social capital forms and is maintained ata steady state level. The resulting network is thechain. The second model uses a congestion function inconjunction with social capital to show a networkemerge that contains links that costlier thanthose in the chain network.