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On Loeb Measure Spaces and their Significance for Non-Cooperative Game Theory

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Current and Future Directions in Applied Mathematics

Abstract

In this expository paper, Loeb measure spaces are constructed on the basis of sequences, and shown to satisfy many useful properties, including some regularity properties of correspondences involving distribution and integration. It is argued that Loeb measure spaces can be effectively and systematically used for the analysis of game-theoretic situations in which “strategic negligibility” and/or “diffuse-ness” of information are substantive and essential issues. Positive results are presented, and the failure of analogous results for identical models based on Lebesgue measure spaces is illustrated by several examples. It is also pointed out that the requirement of Lebesgue measurability, by going against the non-cooperative element in the situation being modelled, is partly responsible for this failure.

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Author information

Authors and Affiliations

  1. Department of Economics, The Johns Hopkins University, Baltimore, MD, 21218, USA

    M. Ali Khan

  2. Department of Mathematics, National University of Singapore, Singapore, 119260

    Yeneng Sun

  3. Cowles Foundation, Yale University, New Haven, CT, USA, 06520

    Yeneng Sun

Authors
  1. M. Ali Khan
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  2. Yeneng Sun
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Editor information

Editors and Affiliations

  1. Department of Mathematics, University of Notre Dame, 46556-5683, Notre Dame, IN, USA

    Mark Alber , Bei Hu  & Joachim Rosenthal ,  & 

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Khan, M.A., Sun, Y. (1997). On Loeb Measure Spaces and their Significance for Non-Cooperative Game Theory. In: Alber, M., Hu, B., Rosenthal, J. (eds) Current and Future Directions in Applied Mathematics. Birkhäuser, Boston, MA. https://doi.org/10.1007/978-1-4612-2012-1_17

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  • DOI: https://doi.org/10.1007/978-1-4612-2012-1_17

  • Publisher Name: Birkhäuser, Boston, MA

  • Print ISBN: 978-1-4612-7380-6

  • Online ISBN: 978-1-4612-2012-1

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