DEPARTMENT OF ECONOMICS WORKING PAPER SERIES Implementing Efficient Graphs in Connection Networks

We consider the problem of sharing the cost of a network that meets the connection demands of a set of agents. The agents simultaneously choose paths in the network connecting their demand nodes. A mechanism splits the total cost of the network formed among the participants. We introduce two new properties of implementation. The first property, Pareto Nash Implementation (PNI), requires that the efficient outcome is always implemented in a Nash equilibrium, and that the efficient outcome Pareto dominates any other Nash equilibrium. The average cost mechanism (AC) and other assymetric variations, are the only rules that meet PNI. These mechanisms are also characterized under Strong Nash Implementation. The second property, Weakly Pareto Nash Implementation (WPNI), requires that the least inefficient equilibrium Pareto dominate any other equilibrium. The egalitarian mechanism (EG), a variation of AC that meets individual rationality, and other assymetric mechanisms are the only rules that meet WPNI and Individual Rationality. PNI and WPNI provide the first economic justification of the Price of Stability (PoS), a seemingly natural measure in the computer science literature but not easily embraced in economics. EG minimizes the PoS across all individually rational mechanisms. JEL classification: C70, C72, D71, D85. ∗We would like to thank our advisor Hervé Moulin for his invaluable insights at the various stages of this paper. This paper benefited from the comments of seminar participants at École Polytechnique, Universitat Autónoma de Barcelona, SED conference in Maastricht, Network Economics conference at LSU and SCW conference in Moscow. Critical comments by Gustavo Bergantinos, Anna Bogomolnaia, Francis Bloch, Anirban Kar, Tim Roughgarden, Sudipta Sarangi, Arunava Sen and Katya Sherstyuk have been very helpful. †University of Hawaii, Department of Economics, 2424 Maile Way, Saunders Hall 542, Honolulu, HI 96822. E-mail: [email protected], Ph: (808) 956-7143. ‡LSU, Department of Economics, 2138 Patrick F. Taylor Hall, Baton Rouge LA 70803 E-mail: [email protected], Ph: (225) 578-3805