Skip to main content
SpringerLink
Log in

Discounted Optimality Criterion

  • Chapter
  • First Online:
Zero-Sum Discrete-Time Markov Games with Unknown Disturbance Distribution

Abstract

We consider the game model

$$\displaystyle \mathscr {G}\mathscr {M}:=(X,A,B,{\mathbb {K}}_{A},{\mathbb {K}}_{B},Q,r) $$

introduced in (1.1). The problems we are concerned with in this chapter are those related to the discounted case, which are summarized as follows.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
eBook
USD 16.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 16.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

References

  1. Ash, R.: Real Analysis and Probability. Academic, New York (1972)

    MATH  Google Scholar 

  2. Bertsekas, D.P., Shreve, S.E.: Stochastic Optimal Control: The Discrete Time Case. Academic, New York (1978)

    MATH  Google Scholar 

  3. Hernández-Lerma, O.: Adaptive Markov Control Processes. Springer, New York (1989)

    Book  Google Scholar 

  4. Hernández-Lerma, O., Lasserre, J.B.: Further Topics on Discrete-Time Markov Control Processes. Springer, New York (1999)

    Book  Google Scholar 

  5. Jaśkiewicz, A., Nowak, A.: Zero-sum ergodic stochastic games with Feller transition probabilities. SIAM J. Control Optim. 45, 773–789 (2006)

    Article  MathSciNet  Google Scholar 

  6. Küenle, H.U.: On Markov games with average reward criterion and weakly continuous transition probabilities. SIAM J. Control Optim. 46, 2156–2168 (2007)

    Article  MathSciNet  Google Scholar 

  7. Nowak, A.: Measurable selection theorems for minimax stochastic optimization problems. SIAM J. Control Optim. 23, 466–476 (1985)

    Article  MathSciNet  Google Scholar 

  8. Schäl, M.: Estimation and control in discounted stochastic dynamic programming. Stochastics 20, 51–71 (1987)

    Article  MathSciNet  Google Scholar 

  9. Van Nunen, J.A.E.E., Wessels, J.: A note on dynamic programming with unbounded rewards. Manag. Sci. 24, 576–580 (1978)

    Article  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mathematics, University of Sonora, Hermosillo, Sonora, Mexico

    J. Adolfo Minjárez-Sosa

Authors
  1. J. Adolfo Minjárez-Sosa
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

Copyright information

© 2020 The Author(s), under exclusive license to Springer Nature Switzerland AG

About this chapter

Check for updates. Verify currency and authenticity via CrossMark

Cite this chapter

Minjárez-Sosa, J.A. (2020). Discounted Optimality Criterion. In: Zero-Sum Discrete-Time Markov Games with Unknown Disturbance Distribution. SpringerBriefs in Probability and Mathematical Statistics. Springer, Cham. https://doi.org/10.1007/978-3-030-35720-7_2

Download citation

Publish with us

Policies and ethics

Search

Navigation