Zero-Sum Discrete-Time Markov Games with Unknown Disturbance Distribution by J. Adolfo Minjárez-Sosa

Author:J. Adolfo Minjárez-Sosa
Language: eng
Format: epub
ISBN: 9783030357207
Publisher: Springer International Publishing

Then Theorem 4.4 yields the following result.

Theorem 4.6

Suppose that Assumptions 4.1 and 4.3 hold. Then for each and ω ∈ Ω,

(a)the game has a value such that

(b) there exists such that, for all x ∈ X, and satisfy

(4.17)

(4.18)

Remark 4.3

Observe that, for each the value function is a random function, and for i = 1, 2, define a random optimal pair of strategies for the game

4.2.1 Empirical Estimation Process

The key points to obtain the approximation of the empirical values to the value are the convergence properties of the empirical distribution. At first glance, from Proposition B.​5, in Appendix B, we have that θ t converges weakly to θ a.s. Thus, for each and continuous and bounded function u on X, (see Definition B.​1)

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