Advertisement

Two-stage noncooperative stochastic games with denumerable state spaces

  • Adam Idzik
Differential Games
Part of the Lecture Notes in Control and Information Sciences book series (LNCIS, volume 22)

Abstract

In this paper we define two-stage noncooperative stochastic games with two optimality criteria: the total discount return criteria and the average return per unit time criterion. We prove, under certain conditions, the existence of an equilibrium strategies for players in such games.

We restrict ourselves to the case of two-person two-stage noncooperative stochastic games only. Generalization to n-person two-stage noncooperative stochastic games does not present any difficulties.

Keywords

Equilibrium Strategy Stochastic Game Equilibrium Policy Markov Game Markov Policy 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. [1]
    FAN, K.: Fixed-point and minimax theorems in locally convex topological linear spaces, Proc. Nat. Acad. Sci. U.S.A. 38(1952), 121–126.Google Scholar
  2. [2]
    FEDERGRUEN, A.: On N-person stochastic games with denumerable state space, Adv. Appl. Prob., 2(1978), 452–471.Google Scholar
  3. [3]
    FURUKAWA, N.: Markovian decision processes with compact action spaces, Ann. of Math. Stat., 43(1972), 1612–1622.Google Scholar
  4. [4]
    IDZIK, A.: On discounted stochastic games, Ph. D. Dissertation, Institute of Mathematics of the Polish Academy of Sciences, Warsaw, 1976.Google Scholar
  5. [5]
    —: Remarks on discounted stochastic games, Transactions of the Eighth Prague Conference 1978, Vol. C, 165–174, Academia, Prague, 1979.Google Scholar
  6. [6]
    MAITRA, A. and T. PARTHASARATHY: On stochastic games, Journ. Opti. Theory and its Appl. 5(1970), 289–300.Google Scholar
  7. [7]
    PARTHASARATHY, K.R.: Probability measures on metric spaces, Academic Press, New York and London, 1967.Google Scholar
  8. [8]
    PARTHASARATHY, T.: Discounted, positive and noncooperative stochastic games, Intern. Journ. of Game Theory, 2(1973), 25–37.Google Scholar
  9. [9]
    — and M. STERN, Markov Games — a survey, University of Illinois, Chicago and Analytic Services Inc., Virginia, 1976.Google Scholar
  10. [10]
    ROSS, S.: Applied Probability Models with Optimization Applications, Holden — Day, San Francisco, 1970.Google Scholar
  11. [11]
    ROYDEN, H.: Real Analysis, 2nd edn., Macmillan, New York, 1968.Google Scholar
  12. [12]
    STERN, M.: On Stochastic Games with Limiting Average Payoff, Ph. D. Dissertation, University of Illinois at Chicago Circle, 1975.Google Scholar

Copyright information

© Springer-Verlag 1980

Authors and Affiliations

  • Adam Idzik
    • 1
  1. 1.Institute of Computer SciencePolish Academy of SciencesWarsaw

Personalised recommendations