  The well-known Braess paradox in congestion games states that adding an
additional road to a transportation network may increase the total travel time,
and consequently decrease the overall efficiency. Motivated by this, this paper
presents a paradox in a similar spirit emerging from another distributed
resource allocation game on networks, namely the power allocation game between
countries developed in \cite{allocation}. The paradox is that by having
additional friends may actually decrease a country's total welfare in
equilibrium. Conditions for this paradox to occur as well as some price of
anarchy results are also derived.
