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

  • M. Ali Khan
  • Yeneng Sun

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.

Keywords

Nash Equilibrium Measure Space Nonstandard Analysis Large Game Perfect Competition 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer Science+Business Media New York 1997

Authors and Affiliations

  • M. Ali Khan
    • 1
  • Yeneng Sun
    • 2
    • 3
  1. 1.Department of EconomicsThe Johns Hopkins UniversityBaltimoreUSA
  2. 2.Department of MathematicsNational University of SingaporeSingapore
  3. 3.Cowles FoundationYale UniversityNew HavenUSA

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