DocumentCode :
800265
Title :
Finite state stochastic games: Existence theorems and computational procedures
Author :
Kushner, Harold J. ; Chamberlain, Stanley G.
Author_Institution :
Brown University, Providence, RI, USA
Volume :
14
Issue :
3
fYear :
1969
fDate :
6/1/1969 12:00:00 AM
Firstpage :
248
Lastpage :
255
Abstract :
Let 
be a Markov process with finite state space and transition probabilities 
depending on ui and 
State 0 is the capture state (where the game ends; 
; 
and 
are the pursuer and evader strategies, respectively, and are to be chosen so that capture is advanced or delayed and the cost ![C_{i^{u,v}} = E[Sum_{0}^{\\infty } k (u(X_{n}), v(X_{n}), X_{n}) | X_{0} = i]](/images/tex/5508.gif)
is minimaxed (or maximined), where 
. The existence of a saddle point and optimal strategy pair or e-optimal strategy pair is considered under several conditions. Recursive schemes for computing the optimal or ε-optimal pairs are given.
be a Markov process with finite state space and transition probabilities depending on u State 0 is the capture state (where the game ends; ; and are the pursuer and evader strategies, respectively, and are to be chosen so that capture is advanced or delayed and the cost is minimaxed (or maximined), where . The existence of a saddle point and optimal strategy pair or e-optimal strategy pair is considered under several conditions. Recursive schemes for computing the optimal or ε-optimal pairs are given.Keywords :
Markov processes; Stochastic differential games; Control engineering; Costs; Delay; Game theory; Markov processes; Military aircraft; Radar detection; Smoothing methods; State-space methods; Stochastic processes;
fLanguage :
English
Journal_Title :
Automatic Control, IEEE Transactions on
Publisher :
ieee
ISSN :
0018-9286
Type :
jour
DOI :
10.1109/TAC.1969.1099172
Filename :
1099172
Link To Document :
