Mechanism design and communication networks
Abstract
This paper characterizes the communication networks for which, in any environment (utilities and beliefs), every incentive compatible social choice function is (partially) implementable. In environments with either common independent beliefs and private values or a bad outcome, we show that any incentive-compatible social choice function is implementable on a given communication network if and only if the network is weakly 2-connected. A network is weakly 2-connected if each player is either directly connected to the designer or indirectly connected to the designer through one of the disjoint path emanating from another player with two disjoint paths to the designer. We couple encryption techniques together with appropriate incentives to secure the transmission of each player's private information to the designer.