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The well-known Braess paradox in congestion games states that adding anadditional road to a transportation network may increase the total travel time,and consequently decrease the overall efficiency. Motivated by this, this paperpresents a paradox in a similar spirit emerging from another distributedresource allocation game on networks, namely the power allocation game betweencountries developed in \cite{allocation}. The paradox is that by havingadditional friends may actually decrease a country's total welfare inequilibrium. Conditions for this paradox to occur as well as some price ofanarchy results are also derived.

The Power Allocation Game on A Network: A Paradox