Difference between revisions of "Recursive game"
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| − | A [[Stochastic game|stochastic game]] with pay-off at the end of a play (see also [[Dynamic game|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 | + | {{TEX|done}} |
| + | A [[Stochastic game|stochastic game]] with pay-off at the end of a play (see also [[Dynamic game|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 [[#References|[1]]] has demonstrated a method of finding both the value of the game and of the optimal strategies. | ||
====References==== | ====References==== | ||
Revision as of 20:47, 14 April 2014
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 |
Comments
References
| [a1] | S. Alpern, "Games with repeated decisions" SIAM J. Control Optim. , 26 : 2 (1988) pp. 468–477 |
How to Cite This Entry:
Recursive game. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Recursive_game&oldid=17733
Recursive game. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Recursive_game&oldid=17733
This article was adapted from an original article by V.K. Domanskii (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article