Social Capital and Conventions: A Social Networks Perspective
We introduce a spatial cost topology in the network formation model analyzed by Jackson and Wolinsky, Journal of Economic Theory 71 (1996), 44--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 network.