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Two-degree-of-freedom Ellsberg urn problem

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Abstract

Traditional model assumes there is only randomness existing in the urn problem. However, if the numbers of the colored balls are unknown, then they should be regarded as uncertain variable. Since a ball is drawn randomly, Ellsberg urn problem is essentially a complicated system with randomness and uncertainty. Instead of psychological experiment, this paper applies uncertainty theory and chance theory to provide a rigorous mathematical method for formulating the general case of a one-degree-of-freedom Ellsberg urn problem. Furthermore, a two-degree-of-freedom Ellsberg urn problem is proposed, and the formulation for the problem is given to deal with three unknown numbers of colored balls.

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Acknowledgements

This work was supported by National Natural Science Foundation of China under Grant No. 61873329.

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Authors and Affiliations

  1. Department of Mathematical Sciences, Tsinghua University, Beijing, 100084, China

    Waichon Lio

  2. College of Systems Engineering, National University of Defense Technology, Changsha, 410073, China

    Guangquan Cheng

Authors
  1. Waichon Lio
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  2. Guangquan Cheng
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Correspondence to Guangquan Cheng.

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Communicated by V. Loia.

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Lio, W., Cheng, G. Two-degree-of-freedom Ellsberg urn problem. Soft Comput 24, 6903–6908 (2020). https://doi.org/10.1007/s00500-019-04327-2

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  • DOI: https://doi.org/10.1007/s00500-019-04327-2

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