A non-cooperative model of network formation with endogenous link strength

Interaction among multiple agents to exchange resources or information is interpreted as network interaction in the field of social sciences. The strategic formation of these network links has been formalized both as cooperative and noncooperative games. This paper analyses the formation of such non-cooperative networks where agents have the discretion to choose as well as decide the level of investment in their connections. This study specifically analyses the case of two-way flow networks where the link between any two agents can be formed and maintained by only one of them whereas the benefit from this link accrues to both the agents. Unlike previous studies, this framework relaxes the assumption of investment decision for an agent to be independent of their partners' level of investment. 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 the stability and aggregate benefit maximizing as the efficiency concept, we show that both the stable and efficient networks are a unique type of flower network. Further, by generalizing the value of paths connecting agents, other networks are also found to be emerging as stable but the efficient architecture still takes the form of the same flower type network, in line with the base model