Mechanism design and communication networks

Abstract

This paper studies a mechanism design model where the players and thedesigner are nodes in a communication network. We characterize the communicationnetworks (directed graphs) for which, in any environment (utilitiesand beliefs), every incentive compatible social choice function is partially implementable.We show that any incentive compatible social choice function isimplementable on a given communication network, in all environments with eithercommon independent beliefs and private values or a worst outcome, if andonly if the network is strongly connected and weakly 2-connected. A networkis 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 thedesigner or indirectly connected to the designer through two disjoint paths, notnecessarily directed. We couple encryption techniques together with appropriateincentives to secure the transmission of each player’s private information to thedesigner.