  We show that an N-person non-cooperative semi-Markov game under limiting
ratio average pay-off has a pure semi-stationary Nash equilibrium. In an
earlier paper, the zero-sum two person case has been dealt with. The proof
follows by reducing such perfect information games to an associated semi-Markov
decision process (SMDP) and then using existence results from the theory of
SMDP. Exploiting this reduction procedure, one gets simple proofs of the
following: (a) zero-sum two person perfect information stochastic (Markov)
games have a value and pure stationary optimal strategies for both the players
under discounted as well as undiscounted pay-off criteria. (b) Similar
conclusions hold for N-person non-cooperative perfect information stochastic
games as well. All such games can be solved using any efficient algorithm for
the reduced SMDP (MDP for the case of Stochastic games). In this paper we have
implemented Mondal's algorithm to solve an SMDP under limiting ratio average
pay-off criterion.
