This paper presented insights into the implementation of transactive
multi-agent systems over flow networks where local resources are decentralized.
Agents have local resource demand and supply, and are interconnected through a
flow network to support the sharing of local resources while respecting
restricted sharing/flow capacity. We first establish a competitive market with
a pricing mechanism that internalizes flow capacity constraints into agents'
private decisions. We then demonstrate through duality theory that competitive
equilibrium and social welfare equilibrium exist and agree under convexity
assumptions, indicating the efficiency of the pricing mechanism. Additionally,
a new social acceptance sharing problem is defined to investigate homogeneous
pricing when the optimal sharing prices at all agents under competitive
equilibrium are always equal for social acceptance. A conceptual computation
method is proposed, prescribing a class of socially admissible utility
functions to solve the social acceptance problem. A special case of
linear-quadratic multi-agent systems over undirected star graphs is provided as
a pedagogical example of how to explicitly prescribe socially admissible
utility functions. Finally, extensive experiments are provided to validate the
results