  These lecture notes attempt a mathematical treatment of game theory akin to
mathematical physics. A game instance is defined as a sequence of states of an
underlying system. This viewpoint unifies classical mathematical models for
2-person and, in particular, combinatorial and zero-sum games as well as models
for investing and betting. n-person games are studied with emphasis on notions
of utilities, potentials and equilibria, which allows to subsume cooperative
games as special cases. The represenation of a game theoretic system in a
Hilbert space furthermore establishes a link to the mathematical model of
quantum mechancis and general interaction systems.
  The notes sketch an outline of the theory. Details are available as a
textbook elsewhere.
