  We continue the study of Bochet et al. and Moulin and Sethuraman on fair
allocation in bipartite networks. In these models, there is a moneyless market,
in which a non-storable, homogeneous commodity is reallocated between agents
with single-peaked preferences. Agents are either suppliers or demanders. While
the egalitarian rule of Bochet et al. satisfies pareto optimality, no envy and
strategyproof, it is not consistent. On the other hand, the work of Moulin and
Sethuraman is related to consistent allocations and rules that are extensions
of the uniform rule. We bridge the two streams of work by introducing the edge
fair mechanism which is both consistent and groupstrategyproof. On the way, we
explore the "price of consistency" i.e. how the notion of consistency is
fundamentally incompatible with certain notions of fairness like Lorenz
Dominance and No-Envy. The current work also introduces the idea of strong
invariance as desideratum for groupstrategyproofness and generalizes the proof
of Chandramouli and Sethuraman to a more broader class of mechanisms. Finally,
we conclude with the study of the edge fair mechanism in a transshipment model
where the strategic agents are on the links connecting different supply/demand
locations.
