  A zero-sum two-person Perfect Information Semi-Markov game (PISMG) under
limiting ratio average payoff has a value and both the maximiser and the
minimiser have optimal pure semi-stationary strategies. We arrive at the result
by first fixing an arbitrary initial state and forming the matrix of
undiscounted payoffs corresponding to each pair of pure stationary strategies
of the two players and proving that this matrix has a pure saddle point.
