<p>In this paper, we study the formation of non-cooperative networks where agents have the discretion to choose with whom to connect as well as decide the level of investment in their connections. We specifically analyze the case of two-way flow networks where the link between any two agents can be formed by only one of them whereas the benefit from this link accrues to both the agents. Also, agents are assumed to have a constraint on the amount of resources that they can allocate across links. In the baseline model, the link strength takes the form of a concave function of individual investments, and agents prefer the most reliable path that maximizes the product of link strengths. Using Nash equilibrium as stability and aggregate benefit maximizing as the efficiency concept, we show that a specific type of flower network emerges as uniquely efficient as well as a Nash network. Further, by generalizing the value of paths connecting agents, other networks are also found to be Nash but the efficient architecture still takes form of the same flower type network, in line with the base model.</p>