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==== | ||
| − | <table><TR><TD valign="top">[1]</TD> <TD valign="top"> H. Everett, "Recursive games" | + | <table><TR><TD valign="top">[1]</TD> <TD valign="top"> H. Everett, "Recursive games" ''in'' Dresher, M. (ed.), Tucker, A. W. (ed.), Wolfe, P. (ed.), ''Contributions to the theory of games III'', Annals of Mathematics Studies '''39''', Princeton Univ. Press (1957) pp. 47–87. {{ZBL|0078.32802}} {{ZBL|0078.31001}}.</TD></TR></table> |
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====Comments==== | ====Comments==== | ||
Latest revision as of 18:27, 3 January 2021
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" in Dresher, M. (ed.), Tucker, A. W. (ed.), Wolfe, P. (ed.), Contributions to the theory of games III, Annals of Mathematics Studies 39, Princeton Univ. Press (1957) pp. 47–87. Zbl 0078.32802 Zbl 0078.31001. |
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