The paper proposes a game of weighted network formation in which each agent has a limited resource to form links of possibly different intensities with other agents and to use for private purposes. We show that every equilibrium is either "reciprocal" or "non-reciprocal". In a reciprocal...

This paper develops a mechanism for a principal to allocate a prize to the most valued agent when agents have a knowledge network. The principal does not know any agent's value but any two linked agents know each other's values. Agents compete for the prize and send costless private messages...