Finite state stochastic games: Existence theorems and computational procedures

Author

Kushner, Harold J. ; Chamberlain, Stanley G.

Author_Institution

Brown University, Providence, RI, USA

Volume

Issue

fYear

1969

fDate

6/1/1969 12:00:00 AM

Firstpage

248

Lastpage

255

Abstract

Let ${X_{n}}$ be a Markov process with finite state space and transition probabilities $p_{ij}(u_{i}, v_{i})$ depending on uiand $v_{i}.$ State 0 is the capture state (where the game ends; $p_{oi} \\equiv \\delta _{oi})$ ; $u = {u_{i}}$ and $v = {v_{i}}$ are the pursuer and evader strategies, respectively, and are to be chosen so that capture is advanced or delayed and the cost $C_{i^{u,v}} = E[Sum_{0}^{\\infty } k (u(X_{n}), v(X_{n}), X_{n}) | X_{0} = i]$ is minimaxed (or maximined), where $k(\\alpha , \\beta , 0) \\equiv 0$ . 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

https://search.isc.ac/dl/search/defaultta.aspx?DTC=49&DC=800265