Division Rules, Network Formation, and the Evolution of Wealth

In our model, each of n> 2 agents is endowed with an exogenous amount of initial wealth. Each individual may establish at most one link with any agent he prefers each period. A surplus will be generated from each link and the agents involved in that link will bargain over its division. The payoffs obtained by an agent at each period will be added to the existing wealth (ideal payoff) level of the agent. Suppose in a society (or in a group of individuals), all agents adhere to a particular division rule. A variety of long-run wealth distributions can arise, depending on the divi-sion rule and initial wealth distribution. These can range from situations where the richest agent remains richest to cases where the poor are continually becom-ing rich. We examine several division rules in detail: egalitarian, equal sacrifice, proportional, dictatorship of the rich, dictatorship of the poor. From the analysis of these cases, we find that two factors determine the long-run wealth distribution: the size of the gain from a link, and the incentive to link to rich or poor