Journal of Optimization Theory and Applications

, Volume 33, Issue 1, pp 145–150 | Cite as

Characterizing properties of the value function of stochastic games

  • S. H. Tijs
  • O. J. Vrieze
Technical Note
  • 43 Downloads

Abstract

In the present note, the axiomatic characterization of the value function of two-person, zero-sum games in normal form by Vilkas and Tijs is extended to the value function of discounted, two-person, zero-sum stochastic games. The characterizing axioms can be indicated by the following terms: objectivity, monotony, and sufficiency for both players; or sufficiency for one of the players and symmetry. Also, a characterization without using the monotony axiom is given.

Key Words

Stochastic games values of stochastic games characterization of the value function 

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References

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    Shapley, L. S.,Stochastic Games, Proceedings of the National Academy of Sciences of the USA, Vol. 39, pp. 1095–1100, 1953.Google Scholar
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    Parthasarathy, T., andStern, M.,Markov Games, A Survey, University of Illinois, Chicago, Illinois, 1976.Google Scholar
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    Vilkas, E. I.,Axiomatic Definition of the Value of a Matrix Game, Theory of Probability and Its Applications, Vol. 8, pp. 304–307, 1963.Google Scholar
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    Tijs, S. H.,A Characterization of the Value of Zero-Sum Two-Person Games, University of Nijmegen, Nijmegen, Holland, Department of Mathematics, Report No. 7632, 1976; Naval Research Logistics Quarterly, Vol. 28, 1981.Google Scholar
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    Tijs, S. H., andVrieze, O. J.,Characterizing Properties of the Value Function of Stochastic Games, Mathematical Center, Amsterdam, Holland, Report No. BW 110/79, 1979.Google Scholar

Copyright information

© Plenum Publishing Corporation 1981

Authors and Affiliations

  • S. H. Tijs
    • 1
  • O. J. Vrieze
    • 2
  1. 1.University of NijmegenNijmegenHolland
  2. 2.Mathematical CenterAmsterdamHolland

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