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:
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1.
Different levels of the tree may have different branching factors.
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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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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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DOI: https://doi.org/10.1007/BF01794430
Keywords
- Artificial Intelligence
- High Probability
- Decision Tree
- Stochastic Process
- Probability Theory