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

Author

Listed:
  • 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)

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 “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.

Suggested Citation

  • KHAN , M. Ali & SUN, Yeneng, 1997. "On Loeb measures spaces and their significance for non-cooperative game theory," LIDAM Discussion Papers CORE 1997012, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    • Handle: RePEc:cor:louvco:1997012
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    File URL: https://sites.uclouvain.be/core/publications/coredp/coredp1997.html
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    Citations

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    Cited by:

    1. M. Ali Khan, 2007. "Perfect Competition," PIDE-Working Papers 2007:15, Pakistan Institute of Development Economics.
    2. Sun, Yeneng, 1998. "A theory of hyperfinite processes: the complete removal of individual uncertainty via exact LLN1," Journal of Mathematical Economics, Elsevier, vol. 29(4), pages 419-503, May.
    3. Rauh, Michael T., 2007. "Nonstandard foundations of equilibrium search models," Journal of Economic Theory, Elsevier, vol. 132(1), pages 518-529, January.
    4. Khan, M. Ali & Sun, Yeneng, 1999. "Non-cooperative games on hyperfinite Loeb spaces1," Journal of Mathematical Economics, Elsevier, vol. 31(4), pages 455-492, May.
    5. Duffie, Darrell & Qiao, Lei & Sun, Yeneng, 2018. "Dynamic directed random matching," Journal of Economic Theory, Elsevier, vol. 174(C), pages 124-183.
    6. Robert M. Anderson & Haosui Duanmu & M. Ali Khan & Metin Uyanik, 2022. "Walrasian equilibrium theory with and without free-disposal: theorems and counterexamples in an infinite-agent context," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 73(2), pages 387-412, April.
    7. Anderson, Robert M. & Duanmu, Haosui & Khan, M. Ali & Uyanik, Metin, 2022. "On abstract economies with an arbitrary set of players and action sets in locally-convex topological vector spaces," Journal of Mathematical Economics, Elsevier, vol. 98(C).

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