  We prove uniqueness and Monge solution results for multi-marginal optimal
transportation problems with a certain class of surplus functions; this class
arises naturally in multi-agent matching problems in economics. This result
generalizes a seminal result of Gangbo and \'Swi\c{e}ch on multi-marginal
problems. Of particular interest, we show that this also yields a partial
generalization of the Gangbo-\'Swi\c{e}ch result to manifolds; alternatively,
we we can think of this as a partial extension of McCann's theorem for
quadratic costs on manifolds to the multi-marginal setting.
  We also show that the class of surplus functions considered here neither
contains, nor is contained in, another class of surpluses studied by the
present author, which also generalized Gangbo and \'Swi\c{e}ch's result.
