B i and Branching Strict Nash Networks in Two-way Flow Models: A Generalized Sufficient Condition

Abstract

Abstract 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.