Identifying the best agent in a network

This paper develops a mechanism for a principal to assign a prize to the most valuable agent from a set of heterogeneously valued agents in a network. The principal does not know the value of any agent. Agents are competing for the prize and they have a "knowledge network": If two agents are linked, they know each other's value for the principal. Each agent sends a costless private message to the principal about her own value and the values of other agents she knows. This message can be truthful or not. However, it is common knowledge that agents can lie about each value only to a certain extent and that agents only lie if lying increases their chances of being selected, otherwise they report truthfully. A mechanism which determines the probability of getting the prize for each agent for each possible message profile is proposed. It is shown that if every agent is linked to at least one other agent in the network, then the mechanism ensures existence of an equilibrium such that the most valuable agent gets the prize with certainty. If the network is complete or a star, then the mechanism ensures that every equilibrium is such that the most valuable agent gets the prize with certainty.