  Systems of cooperation and interaction are usually studied in the context of
real or complex vector spaces. Additional insight, however, is gained when such
systems are represented in vector spaces with multiplicative structures, i.e.,
in algebras. Algebras, on the other hand, are conveniently viewed as polynomial
algebras. In particular, basic interpretations of natural numbers yield natural
polynomial algebras and offer a new unifying view on cooperation and
interaction. For example, the concept of Galois transforms and zero-dividends
of cooperative games is introduced as a nonlinear analogue of the classical
Harsanyi dividends. Moreover, the polynomial model unifies various versions of
Fourier transforms. Tensor products of polynomial spaces establish a unifying
model with quantum theory and allow to study classical cooperative games as
interaction activities in a quantum-theoretic context.
