Note on recursive games

Recursive games are stochastic games with the property that all payoffs in non-absorbing states axe equal to zero. For the zero-sum two-player model with finite state and action spaces, we present a new proof for the existence of the limiting average value v and of stationary limiting average epsilon-optimal strategies. If we take an arbitrary sequence of stationary beta-discounted optimal strategies x(beta), converging to x1 as beta tends to 1, then a limiting average epsilon-optimal strategy for player 1 is given by: in state s play x(s)1 if v(s) less-than-or-equal-to 0, otherwise play x(s)beta (beta sufficiently close to 1).