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

In: Current and Future Directions in Applied Mathematics

Author

Listed:
  • M. Ali Khan

    (The Johns Hopkins University, Department of Economics)

  • Yeneng Sun

    (National University of Singapore, Department of Mathematics
    Yale University, Cowles Foundation)

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.

Suggested Citation

  • M. Ali Khan & Yeneng Sun, 1997. "On Loeb Measure Spaces and their Significance for Non-Cooperative Game Theory," Springer Books, in: Mark Alber & Bei Hu & Joachim Rosenthal (ed.), Current and Future Directions in Applied Mathematics, pages 183-218, Springer.
    • Handle: RePEc:spr:sprchp:978-1-4612-2012-1_17
    DOI: 10.1007/978-1-4612-2012-1_17
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