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Decision Theory with a Hilbert Space as Possibility Space

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  • Eichberger, Jürgen
  • Pirner, Hans Jürgen

Abstract

In this paper, we propose an interpretation of the Hilbert space method used in quantum theory in the context of decision making under uncertainty. For a clear comparison we will stay as close as possible to the framework of SEU suggested by Savage (1954). We will use the Ellsberg (1961) paradox to illustrate the potential of our approach to deal with well-known paradoxa of decision theory.

Suggested Citation

  • Eichberger, Jürgen & Pirner, Hans Jürgen, 2017. "Decision Theory with a Hilbert Space as Possibility Space," Working Papers 0637, University of Heidelberg, Department of Economics.
    • Handle: RePEc:awi:wpaper:0637
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    References listed on IDEAS

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    1. Gilboa, Itzhak & Schmeidler, David, 1989. "Maxmin expected utility with non-unique prior," Journal of Mathematical Economics, Elsevier, vol. 18(2), pages 141-153, April.
    2. Daniel Kahneman & Amos Tversky, 2013. "Prospect Theory: An Analysis of Decision Under Risk," World Scientific Book Chapters, in: Leonard C MacLean & William T Ziemba (ed.), HANDBOOK OF THE FUNDAMENTALS OF FINANCIAL DECISION MAKING Part I, chapter 6, pages 99-127, World Scientific Publishing Co. Pte. Ltd..
    3. Schmeidler, David, 1989. "Subjective Probability and Expected Utility without Additivity," Econometrica, Econometric Society, vol. 57(3), pages 571-587, May.
    4. Vyacheslav I. Yukalov & Didier Sornette, 2010. "Mathematical Structure Of Quantum Decision Theory," Advances in Complex Systems (ACS), World Scientific Publishing Co. Pte. Ltd., vol. 13(05), pages 659-698.
    5. Diederik Aerts & Sandro Sozzo, 2011. "Contextual Risk and Its Relevance in Economics," Papers 1105.1812, arXiv.org.
    6. Daniel Ellsberg, 1961. "Risk, Ambiguity, and the Savage Axioms," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 75(4), pages 643-669.
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    More about this item

    Keywords

    Decision theory; uncertainty; Ellsberg paradox; quantum theory; Hilbert space; possibility space;
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