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A weighted directed graph G IS a triple (V, A . g) where (V. A) IS a directed graph and g is a n arbitrary real-valued function defined on the arc set A. Let G be a strongly-connected, simple weighted directed graph. We say th a t G is max-balanced if fo r every nontrivial ~ubset of th e vertices W, the maxImum weight over arcs leavin g W equals th e maximum weIght over arcs e ntering W. We show that there ex ists a (up to an addItIve con~tant) un iq ue potential p, for ( E V such that (V, A,doi:10.1287/moor.16.1.208 fatcat:xg4pmchy4vez5nn2vlwspzbjxu