Realizing e ffi cient outcomes in cost spanning problems ∗ † Gustavo Bergantiños Universidade de Vigo Juan J. Vidal-Puga ‡ Universidade de Vigo February 26, 2004 Abstract We propose a simple non-cooperative mechanism of network formation in cost spanning tree problems. The only subgame equilibrium payoff is efficient. Moreover, we extend the result to the case of budget restrictions. The equilibrium payoff can them be easily adapted to the framework of Steiner trees. Keywords: efficiency, cost spanning tree problem, cost allocation, network formation, subgame perfect equilibrium, budget restrictions, Steiner trees 1 Introduction Many problems involving network formation have been studied in the opera- tional research and the economic literature. The most explored issues in oper- ational research are the design of efficient algorithms and their computational complexity. The economic literature focuses on aspects such like the cost shar- ing of the network and the design of mechanisms trying to explain the way in which the network forms. In this paper we focus in the cost sharing aspect. In particular, we study cost spanning tree problems (cstp). Consider that a group of agents, located at different geographical places, want some particular service which can only be provided by a common supplier, called the source. Agents will be served through connections which entail some cost. However, they do not care whether they are connected directly or indirectly to the source. There are many economic situations that can be modeled in this way. For instance, several towns may draw power from a common power plant, and hence ∗ Latest version at http://webs.uvigo.es/vidalpuga/ † Finantial support from the Spanish Ministerio de Educación y Ciencia and FEDER through grant BEC2002-04102-c02-01 and Xunta de Galicia through grant PGIDIT03PXIC30002PN is gratefully acknowledged. ‡ Corresponding author. Email: vidalpuga@uvigo.es 1