Ugo Bolletta : ugo.bolletta[at]univ-amu.fr
Mathieu Faure : mathieu.faure[at]univ-amu.fr
Often a network is characterized not only by who is linked to whom but also by the intensity of the links. We analyze a network formation model in which homogenous agents have a limited resource (e.g. time) which they can use to form links of possibly different intensity with other agents (e.g. friendships) and which they can invest into themselves. We show that in equilibrium an agent either has no links, belongs to a "reciprocal" component or to a "non-reciprocal" component (maximal connected subgraph of the network). In a reciprocal component, any two agents invest equally into their link and self-investment is identical across the group. In a non-reciprocal component, every agent is either a "high intensity" agent or a "low intensity" agent. High intensity agents are only linked to low intensity agents and vice versa. A high intensity agent always invests more into a link than her counterpart low intensity agent and also chooses a higher self-investment. We show that in equilibrium any component in which every agent has the same number of links must be reciprocal; any component of more than two agents in which at least one agent has only one link must be non-reciprocal. Welfare-maximizing components are reciprocal but feature a lower self-investment than in reciprocal equilibrium because of positive externalities from link investments.