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On Loeb measures spaces and their significance for non-cooperative game theory

Listed author(s):
  • KHAN , M. Ali

    (Department of Economics, The Johns Hopkins University, Baltimore)

  • SUN, Yeneng

    (Department of Mathematics, National University of Singapore, Singapore and Cowles Fondation, Yale University, New Haven)

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 “diffuseness” 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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Paper provided by Université catholique de Louvain, Center for Operations Research and Econometrics (CORE) in its series CORE Discussion Papers with number 1997012.

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Date of creation: 01 Feb 1997
Handle: RePEc:cor:louvco:1997012
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