  In this paper we address a class of replicator dynamics, referred as
polymatrix replicators, that contains well known classes of evolutionary game
dynamics, such as the symmetric and asymmetric (or bimatrix) replicator
equations, and some replicator equations for $n$-person games. Polymatrix
replicators form a simple class of algebraic o.d.e.'s on prisms (products of
simplexes), which describe the evolution of strategical behaviours within a
po\-pu\-lation stratified in $n\geq 1$ social groups.
  In the 80's Raymond Redheffer et al. developed a theory on the class of
stably dissipative Lotka-Volterra systems. This theory is built around a
reduction algorithm that "infers" the localization of the system' s attractor
in some affine subspace. It was later proven that the dynamics on the attractor
of such systems is always embeddable in a Hamiltonian Lotka-Volterra system.
  In this paper we extend these results to polymatrix replicators.
