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On Milnor's classes “L” and “D”

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Abstract

A twenty-one player counterexample is presented which disposes of two questions raised by J. W. Milnor in 1952 concerning the existence of certain pre-solutions, based on plausible lower and upper bounds to what a coalition should expect to receive in a cooperative game in characteristic function form. In the counterexample, the lower-bound set, known as “L”, is empty, and the upper-bound set, known as “D”, contains no efficient outcomes.

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Authors and Affiliations

  1. Dept. of Economics, Toyama University, Gofuku, 930, Toyama City, Japan

    K. Kikuta

  2. Dept. of Mathematics, University of California, 90024, Los Angeles, CA, USA

    L. S. Shapley

Authors
  1. K. Kikuta
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  2. L. S. Shapley
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Kikuta, K., Shapley, L.S. On Milnor's classes “L” and “D”. Int J Game Theory 15, 231–235 (1986). https://doi.org/10.1007/BF01769387

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  • DOI: https://doi.org/10.1007/BF01769387

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