Social capital and conventions: A social networks perspective

                         Johnson, Cathleen Amanda; PhD

                         ECONOMICS, THEORY (0511)

                         We introduce a spatial cost topology in the network formation model analyzed by Jackson and Wolinsky,
                         <italic>Journal of Economic Theory</italic> <bold> 71</bold> (1996), 44&ndash;74. This cost topology
                         might represent geographical, social, or individual differences. It describes variable costs of establishing
                         social network connections. Participants form links based on a cost-benefit analysis. We examine the
                         pairwise stable networks within this spatial environment. Incentives vary enough to show a rich pattern of
                         emerging behavior. We also investigate the subgame perfect implementation of pairwise stable and
                         efficient networks. We construct a multistage extensive form game that describes the formation of links in
                         our spatial environment. Finally, we identify the conditions under which the subgame perfect Nash
                         equilibria of these network formation games are stable. We analyze the dynamic implications of learning in
                         a large population coordination game where both the actions of the players and the communication
                         network evolve over time. Cost considerations of social interaction are incorporated by considering a
                         circular model with endogenous neighborhoods, meaning that the locations of the players are fixed but
                         players can create their own communication network. The dynamic process describing medium-run
                         behavior is shown to converge to an absorbing state, which may be characterized by coexistence of
                         conventions. In the long run, when mistake probabilities are small but nonvanishing, coexistence of
                         conventions is no longer sustainable as the risk-dominant convention becomes the unique stochastically
                         stable state. We create and investigate a system that is capable of observing the accumulation of social
                         capital and the effect of social capital accumulation on behavior of individually rational players. In the first
                         model, we develop a restricted system to show that social capital forms and is maintained at a steady state
                         level. The resulting network is the chain. The second model uses a congestion function in conjunction
                         with social capital to show a network emerge that contains links that costlier than those in the chain


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