We thank Dirk Bergemann, Subir Bose, Martin Cripps, Gianni De Fraja, Johannes Hörner, Stefano Lovo, Claudio Mezzetti, Jérôme Renault, Karl H. Schlag, Sylvain Sorin, Nicolas Vieille, Yannick Viossat, Piercarlo Zanchettin, and seminar participants at several seminars and conferences. We owe this piece of work to a discussion between Murali Agastya and one of the author a few years ago. Ludovic Renou thanks the hospitality of Fuqua Business School at Duke University. Tristan Tomala gratefully acknowledges the support of the HEC foundation.
Mechanism design and communication networks
Article first published online: 3 OCT 2012
Copyright © 2012 Ludovic Renou and Tristan Tomala
Volume 7, Issue 3, pages 489–533, September 2012
How to Cite
Renou, L. and Tomala, T. (2012), Mechanism design and communication networks. Theoretical Economics, 7: 489–533. doi: 10.3982/TE921
- Issue published online: 3 OCT 2012
- Article first published online: 3 OCT 2012
- Submitted 2011-1-7. Final version accepted 2011-8-2. Available online 2011-8-2.
- Mechanism design;
- Bayesian equilibrium;
- communication networks;
- secure transmission
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, not necessarily directed. We couple encryption techniques together with appropriate incentives to secure the transmission of each player's private information to the designer.