Recursive game

A stochastic game with pay-off at the end of a play (see also Dynamic game). Since a recursive game can be endless, it is essential to determine the pay-off of the players in the case of infinite plays. An analysis of any Shapley game can be reduced to an analysis of a certain recursive game, but because of the possibility of infinite plays, research on recursive games is generally more complicated than research on stochastic games. Any zero-sum two-person finite recursive game has a value and both players have stationary $\epsilon$-optimal strategies. H. Everett [1] has demonstrated a method of finding both the value of the game and of the optimal strategies.

References

[1]	H. Everett, "Recursive games" H.W. Kuhn (ed.) A.W. Tucker (ed.) , Contributions to the theory of games , 3 , Princeton Univ. Press (1957) pp. 47–87

References

[a1]	S. Alpern, "Games with repeated decisions" SIAM J. Control Optim. , 26 : 2 (1988) pp. 468–477