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Classification and Basic Tools

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Book cover Stochastic Games and Applications

Part of the book series: NATO Science Series ((ASIC,volume 570))

Abstract

A stochastic game is a multi-stage game played in discrete time where, at each stage, the stage game played depends upon a parameter called state. The value of the state evolves as a function of its current value and the actions of the players. Let I be the finite set of players and S be the set of states. For each state z in S, an I-player normal form game is specified by action sets A i(z) for each player i in I and reward functions r i(z,.), i in I, from the set of action profiles at z, A (z) = Π iɛI A i(z) to the reals, ℝ. In addition, for any pair consisting of a state z in S and an action profile a in A(z), a probability p(.|z,a) on S describes the random transition.

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Author information

Authors and Affiliations

  1. Université P. et M. Curie and École Polytechnique, Paris, France

    Sylvain Sorin

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  1. Sylvain Sorin
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Editor information

Editors and Affiliations

  1. Institute of Mathematics and Center for Rationality and Interactive Decision Theory, Hebrew University of Jerusalem, Jerusalem, Israel

    Abraham Neyman

  2. Université Pierre et Marie Curie and École Polytechnique, Paris, France

    Sylvain Sorin

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Sorin, S. (2003). Classification and Basic Tools. In: Neyman, A., Sorin, S. (eds) Stochastic Games and Applications. NATO Science Series, vol 570. Springer, Dordrecht. https://doi.org/10.1007/978-94-010-0189-2_3

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  • DOI: https://doi.org/10.1007/978-94-010-0189-2_3

  • Publisher Name: Springer, Dordrecht

  • Print ISBN: 978-1-4020-1493-2

  • Online ISBN: 978-94-010-0189-2

  • eBook Packages: Springer Book Archive

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