Asymmetric flow networks

This paper provides a new model of network formation that bridges the gap between the two benchmark models by Bala and Goyal, the one-way ‡ow model, and the two-way ‡ow model, and includes both as particular extreme cases. As in both benchmark models, in what we call an “asymmetric ‡ow”network a link can be initiated unilaterally by any player with any other, and the ‡ow through a link towards the player who supports it is perfect. Unlike those models, in the opposite direction there is friction or decay. When this decay is complete there is no ‡ow and this corresponds to the one-way ‡ow model. The limit case when the decay in the opposite direction (and asymmetry) disappears, corresponds to the two-way ‡ow model. We characterize stable and strictly stable architectures for the whole range of parameters of this “intermediate” and more general model. We also prove the convergence of Bala and Goyal’s dynamic model in this context. JEL Classi…cation Numbers: A14, C72, D20, J00 Key words: Non-cooperative network formation, Asymmetric ‡ow, Stability, E¢ ciency, Dynamics. We thank Coralio Ballester and Francesco Feri for helpful comments. Of course, the usual disclaimer applies. This research is supported by the Spanish Ministerio de Economía y Competitividad under projects ECO2009-11213 and ECO2009-07939, co-funded by the ERDF. Both authors also bene…t from the Basque Government’s funding to Grupos Consolidados GIC07/146-IT-377-07 and GIC07/22-IT-223-07. yBRiDGE group (http://www.bridgebilbao.es), Departamento de Fundamentos del Análisis Económico I, Universidad del País Vasco UPV/EHU, Avenida Lehendakari Aguirre 83, 48015 Bilbao, Spain; [email protected]. zBRiDGE group (http://www.bridgebilbao.es), Departamento de Economía Aplicada IV, Universidad del País Vasco UPV/EHU, Avenida Lehendakari Aguirre 83, 48015 Bilbao, Spain; [email protected].