A noncooperative model of network formation with decreasing productivity

This paper develops a model of noncooperative network formation. Link formation is two-sided. Information flow is two-way. The paper is based on Bala and Goyal (2000) with the following difference in assumption: the value of information decays as it flows through each agent, and the decay is increasing and concave in the number of his links. Thus, an agent may choose to avoid accessing an agent who possess many links since he is aware of the decay incurred through this agent. This avoidance leads to two particular results in the analysis of Nash networks: (1) Nash networks are not always connected; (2) Nash networks do not exist under some parameters. Since disconnectedness is reminiscent of a common feature of real-world network, the model may explain why real-world networks may exhibit this feature even when there is no heterogeneity among agents. Discussion on this insight is provided.