  We consider a nonlinear extension of the generalized network flow model, with
the flow leaving an arc being an increasing concave function of the flow
entering it, as proposed by Truemper and Shigeno. We give a polynomial time
combinatorial algorithm for solving corresponding flow maximization problems,
finding an epsilon-approximate solution in O(m(m+log n)log(MUm/epsilon))
arithmetic operations and value oracle queries, where M and U are upper bounds
on simple parameters. This also gives a new algorithm for linear generalized
flows, an efficient, purely scaling variant of the Fat-Path algorithm by
Goldberg, Plotkin and Tardos, not using any cycle cancellations.
  We show that this general convex programming model serves as a common
framework for several market equilibrium problems, including the linear Fisher
market model and its various extensions. Our result immediately extends these
market models to more general settings. We also obtain a combinatorial
algorithm for nonsymmetric Arrow-Debreu Nash bargaining, settling an open
question by Vazirani.
