Stochastic games. (English) Zbl 1180.91042

Shapley, L. S.

Neyman, Abraham (ed.) et al., Stochastic games and applications. Lectures given at the NATO Advanced Study Institute on “Stochastic games and applications”, Stony Brook, NY, USA, July 1999. On the occasion of L. S. Shapley’s eightieth birthday. Dordrecht: Kluwer Academic Publishers (ISBN 1-4020-1492-9/hbk). NATO ASI Ser., Ser. C, Math. Phys. Sci. 570, 1-7 (2003).

This is a survey on the general theory of stochastic games which originally appeared in [L. S. Shapley, Proc. Natl. Acad. of Sci. USA, 39, 1095–1100 (1953; Zbl 0051.35805)]. The author first recalls the notion of stochastic games and defines the notion of stationary strategies, namely those which prescribe for a player the same probabilities for his choices every time the same position is reached. Then he proves the existence of a solution. More precisely he gives the value of the game and the existence of optimal strategies in every game obtained by specifying a starting position. Finally he gives some examples and applications of these results.
For the entire collection see [Zbl 1027.00040].

Reviewer: Jean-Pierre Lepeltier (Le Mans)

MSC:

91A15

Stochastic games, stochastic differential games

Keywords:

mixed strategies; stationary strategies

Citations:

Zbl 0051.35805