This paper brings together analyses of Two-way Flow Strict Nash networks under exclusive player heterogeneity assumption and exclusive partner heterogeneity assumption. This is achieved through examining how the interactions between these two assumptions influence important properties of Strict Nash networks. Built upon the findings of Billand et al (2011) and Galleotti et al (2006), which assume exclusive partner heterogeneity and exclusive player heterogeneity respectively, I provide a proposition that generalizes the results of these two models by stating that: (i) Strict Nash network consists of multiple non-empty components as in Galleotti et al (2006), and (ii) each non-empty component is a branching or B i network as in Billand et al (2011). This proposition requires that a certain restriction on link formation cost (called Uniform Partner Rankng), which encloses exclusive partner heterogeneity and exclusive player heterogeneity as a specific case, is satisfied. In addition, this paper shows that value heterogeneity plays a relatively less important role in changing the shapes of Strict Nash networks. JEL Classification : C72, D85

Bi and branching networks are two classes of minimal networks often found in the literatures of two-way flow Strict Nash networks. Why so? In this paper, we answer this question by establishing a generalized condition that holds together many models in the literature, and then show that this condition is sufficient to guarantee their common result: every non-empty component of minimal SNN is either a branching or Bi network. This paper, therefore, contributes to the literature by providing a generalization of several existing works in the literature of two-way flow Strict Nash networks.Abstract B i and branching networks are two classes of minimal networks often found in the literatures of two-way flow Strict Nash networks. Why so? In this paper, we answer this question by establishing a generalized condition that holds together many models in the literature, and then show that this condition is sufficient to guarantee their common result: every non-empty component of minimal SNN is either a branching or B i network. This paper, therefore, contributes to the literature by providing a generalization of several existing works in the literature of two-way flow Strict Nash networks.JEL Classification: C72, D85 -for their excellent helps that substantially save my time for this research. In the previous years I also have several other assistants beside these four. While their names are not mentioned to save space, my gratitude to their works is expressed here.

Bi and branching networks are two classes of minimal networks often found in the literature of two-way flow Strict Nash networks. Why so? In this paper, we answer this question by establishing a generalized condition that holds together several models in the literature, and then show that this condition is sufficient to guarantee their common result: every non-empty component of minimal Strict Nash network is either a branching or Bi network. This paper, therefore, contributes to the literature of two-way flow Strict Nash networks by merging together several existing works.

In this note, I study the roles of value heterogeneity-i.e., agents are heterogeneous in terms of values of nonrival information thay they possessed-in determining the shapes of two-way flow Strict Nash networks when small amount of decay is present. I do so by extending the two-way flow network with small decay of De Jaegher and Kamphorst (J ECON BEHAV ORGAN, 2015). Results of this extension shows that the effects of value heterogeneity on Strict Nash networks, when small decay is present, largely resemble the effects of heterogeneity in link formation cost-without decay-found in the literature. Another surprising finding is that value heterogeneity can extend the diameters of Strict Nash networks without changing any other properties. In the discussion section of this note, I relate this finding to two well-known concepts in the studies of social networks-small world and preferential attachment.

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