Secure communication: A mechanism design approach

This paper considers a mechanism design model where a designer, or receiver, takes an action based on the information received by multiple players, or senders. The agents, senders and receiver, communicate in a fixed directed network. We characterize the communication networks for which, in any environment (utilities and beliefs) with a worst action, every incentive compatible social choice function is implementable on the network. We show that this holds true if and only if the network is weakly 2-connected. A network is weakly 2-connected if for each player i, who is not directly connected to the designer, there exists a player k and two vertex-disjoint paths from k to the designer such that i lies on one of the two paths. We couple encryption techniques together with appropriate incentives to secure the transmission of each player's private information to the designer.