Asymmetric flow networks

Abstract

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.

From bilateral two-way to unilateral one-way flow link-formation

“…16 A similar transition between the two models by Bala and Goyal (2000a) studied in Olaizola and Valenciano (2014) is obtained by assuming:…”

“…In two previous papers we have studied two transitional models. Olaizola and Valenciano (2014) introduces a model that integrates Bala and Goyal's one-way and two-way flow models without decay as particular extreme cases of a more general one. Olaizola and Valenciano (2015a) provides a new hybrid model which has a variant of Jackson and Wolinsky's connections model without decay and Bala and Goyal's two-way flow model as extreme cases.…”

A unifying model of strategic network formation

“…In this case, the dominant structure is g ks . Thus v(g ks ) is given by (9), with (10). Thus, comparing this value with that of v(g ks+1 ) and v(g ks 1 ), we have…”

“…9 Note that if ji 2 g, then ji 2 g i . 10 Although other interpretations are possible, in general, we give preference to the interpretation in terms of information.…”

“…Given a strategy pro…le g 2 G N and i 2 N , g i denotes the N nfig strategy pro…le that results by eliminating g i in g, i.e. all links in which player i invests 9 , and (g i ; g 0 i ), where g 0 i 2 G i , denotes the strategy pro…le that results from replacing g i by g 0 i in g. Let g be a strategy pro…le representing the links invested in by each player. The following is generally assumed:…”