We examine the dynamic formation and stochastic evolution of networks connecting individuals. The payoff to an individual from an economic or social activity depends on the network of connections among individuals. Over time individuals form and sever links connecting themselves to other individuals based on the improvement that the resulting network offers them relative to the current network. In addition to intended changes in the network there is a small probability of unintended changes or errors. Predictions can be made regarding the likelihood that the stochastic process will lead to any given network at some time, where the stochastic process selects from among the statically stable networks and cycles. We apply these results to examples including the Gale-Shapley marriage problem. Thus the paper achieves two goals. First, it outlines a dynamic solution concept for networks. Second, it applies this concept to matching problems. Journal of Economic Literature Classification Numbers: A14, D20, J00. (C) 2002 Elsevier Science (USA).
