Stochastic Games and Mathematical Programming

Abstract

The two-person zero-sum Markov game is investigated. This game is defined by the five-tuple (E,A,B,p,r), where

• E is the finite state space;

• $A = \begin{array}{*{20}{c}} U \\ {i\varepsilon E} \end{array})$ A(i) is the finite action space for player I;

• $B = \begin{array}{*{20}{c}} U \\ {i\varepsilon E} \end{array}$ B(i) is the finite action space for player II;

• p is a transition probability from ExAxB to E;

• r is a real-valued reward function on ExAxB.