Mechanism design and communication networks

This paper studies a mechanism design model where the players and the designer are nodes in a communication network. We characterize the communication networks (directed graphs) for which, in any environment (utilities and beliefs), every incentive compatible social choice function is partially implementable. We show that any incentive compatible social choice function is implementable on a given communication network, in all environments with either common independent beliefs and private values or a worst outcome, if and only if the network is strongly connected and weakly 2-connected. A network is strongly connected if for each player, there exists a directed path to the designer. It is weakly 2-connected if each player is either directly connected to the designer or indirectly connected to the designer through two disjoint paths, {\em not necessarily directed}. We couple encryption techniques together with appropriate incentives to secure the transmission of each player's private information to the designer.