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Asymptotic properties of levelregular decision trees with randomly evaluated leaves
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  • Published: September 1989

Asymptotic properties of levelregular decision trees with randomly evaluated leaves

  • Ingo Althöfer1 

Probability Theory and Related Fields volume 80, pages 381–394 (1989)Cite this article

  • 52 Accesses

  • 1 Citations

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Summary

Game trees are an important model of decision-making situations, both in artificial intelligence and decision analysis. The model most frequently investigated in theoretical research consists of a uniform tree of heighh and a constant branching factorb, where the terminal positions are assigned the values of independent, identically distributed random variables [1, 3–10]. Our paper investigates two generalizations:

  1. 1.

    Different levels of the tree may have different branching factors.

  2. 2.

    The preferences of the two players may no longer be totally opposite.

Our result concerns evaluation functions with a finite range of values. We prove that the induced (minimax) value of the tree's root is with high probability one of only two “neighbouring” values. Such a result does not hold for decision trees with three players.

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References

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Author information

Authors and Affiliations

  1. Fakultät für Mathematik, Universität Bielefeld, Postfach 8640, D-4800, Bielefeld 1, Federal Republic of Germany

    Ingo Althöfer

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  1. Ingo Althöfer
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Cite this article

Althöfer, I. Asymptotic properties of levelregular decision trees with randomly evaluated leaves. Probab. Th. Rel. Fields 80, 381–394 (1989). https://doi.org/10.1007/BF01794430

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  • Received: 10 April 1987

  • Revised: 19 November 1987

  • Issue Date: September 1989

  • DOI: https://doi.org/10.1007/BF01794430

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Keywords

  • Artificial Intelligence
  • High Probability
  • Decision Tree
  • Stochastic Process
  • Probability Theory
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