The Evolution of Social and Economic Networks
We examine the dynamic formation and stochastic evolution of networks connecting individuals whose payoffs from an economic or social activity depends on the network structure in place. Over time, individuals form and sever links connecting themselves to other individuals based on the improvement the resulting network offers them relative to the current network. Such a process creates a sequence of networks that we call an 'improving path'. The changes made along an improving path make the individuals, who added or deleted the relevant link(s) at each date, better off. Such sequences of networks can cycle, and we study conditions on underlying allocation rules that characterize cycles. Building on an understanding of improving paths, we consider a stochastic evolutionary process where in addition to intended changes in the network there is a small probability of unintended changes or errors. Predictions can be made regarding the relative likelihood that the stochastic evolutionary process will lead to any given network at some time. The evolutionary process selects from among the statically stable networks and cycles. We show that in some cases, the evolutionary process selects inefficient networks even though eAEcient ones are statically stable. We apply these results to the matching literature to show that there are contexts in which the evolutionarily stable networks coincide with the core stable networks, and thus achieve eAEciency.