  An interaction system has a finite set of agents that interact pairwise,
depending on the current state of the system. Symmetric decomposition of the
matrix of interaction coefficients yields the representation of states by
self-adjoint matrices and hence a spectral representation. As a result,
cooperation systems, decision systems and quantum systems all become visible as
manifestations of special interaction systems. The treatment of the theory is
purely mathematical and does not require any special knowledge of physics. It
is shown how standard notions in cooperative game theory arise naturally in
this context. In particular, Fourier transformation of cooperative games
becomes meaningful. Moreover, quantum games fall into this framework. Finally,
a theory of Markov evolution of interaction states is presented that
generalizes classical homogeneous Markov chains to the present context.
